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The global geometry of moduli spaoes

Research Project

Project/Area Number 16204001
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHokkaido University

Principal Investigator

NAKAMURA Iku  Hokkaido University, Faculty of Science,Hokkaido University, Professor (50022687)

Co-Investigator(Kenkyū-buntansha) YOSHIOKA Kota  Kobe University, Faculty of Science, Professor (40274047)
KONDO Shigeyuki  Nagoya University, Graduate School of Mathematics, Professor (50186847)
WENG Lin  Kyushu University, Faculty of Mathematics, Associate Professor (60304002)
KATO Fumiharu  Kyoto University, Department of Mathematics, Associate Professor (50294880)
MATSUMOTO Keiji  Hokkaido University, Faculty of Science, Associate Professor (30229546)
小野 薫  北海道大学, 大学院理学研究院, 教授 (20204232)
山下 博  北海道大学, 大学院・理学研究科, 教授 (30192793)
宮岡 洋一  東京大学, 大学院・数理科学研究科, 教授 (50101077)
石田 正典  東北大学, 大学院・理学研究科, 教授 (30124548)
Project Period (FY) 2004 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥43,680,000 (Direct Cost: ¥33,600,000、Indirect Cost: ¥10,080,000)
Fiscal Year 2007: ¥10,400,000 (Direct Cost: ¥8,000,000、Indirect Cost: ¥2,400,000)
Fiscal Year 2006: ¥10,400,000 (Direct Cost: ¥8,000,000、Indirect Cost: ¥2,400,000)
Fiscal Year 2005: ¥10,400,000 (Direct Cost: ¥8,000,000、Indirect Cost: ¥2,400,000)
Fiscal Year 2004: ¥12,480,000 (Direct Cost: ¥9,600,000、Indirect Cost: ¥2,880,000)
KeywordsMcKay correspondence / Moduli / Compactification / Rigid geometry / p-adic geometry / Mumford fake projective plane / K3 Surfaces / L-function / アーベル多様体 / flux予想 / 安定性 / モジュライのコンパクト化 / 複素超球の算術商 / テータ関数 / モジュライ空間 / 群軌道のヒルベルト・スキーム / 3次曲面,複素超球 / 2次超曲面
Research Abstract

Nakamura proved a new theorem on McKay correspondence of a simple singularity C2/G, G being a finite group of SL(2,C). The theorem shows certain natural modules V and Vdagger have simple structures. Among others, the structure of Vdagger explains completely the known bijetive correspondence of the extended Dynkin diagram and all the irreducible representations of G.. The paper is now in print. He also proved an important vanishing theorem for degenerate quasi-abelian varieties.
Weng is constructing a new important theory of geometric class field theory, which is modeled after Mumford's stability of GIT, Seshadri-Narashiman's theory of unitary vector bundles. In this program he defined nonabelian L-functions, and in some cases he proved a theorem analogous to Riemann hypothesis.
Kato studied with Fujiwara the fundamental theory of p-adic geometry and rigid geometry. He proved also that Mumford fake projective plane and the other known fake projective planes are among Shimura varieties.
Kondo constructed a uniformization by a 5-dimensional complex ball of the moduli of ordered 8 points of the projective line, by using Borcherds modular forms.
Matsumoto gave a very precise description of a link and its complement in S3 by using real theta functions.
Yoshioka proved a formula of counting the number of instantons on certain complex surfaces with Nakajima.

Report

(5 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (101 results)

All 2008 2007 2006 2005 2004 Other

All Journal Article (60 results) (of which Peer Reviewed: 18 results) Presentation (33 results) Book (8 results)

  • [Journal Article] McKay correspondence.2008

    • Author(s)
      中村 郁
    • Journal Title

      Proceedings of the Conference in honor of John McKay (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Mckay correspondence2008

    • Author(s)
      Iku Nakamura
    • Journal Title

      Proceedings of the Conference in honor of John McKay (Printing)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] McKay correspondence,2008

    • Author(s)
      中村 郁
    • Journal Title

      Proceedings of the Conference in honor of John McKay (印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A geometric approach to L-functions2007

    • Author(s)
      翁 林
    • Journal Title

      The Conference on $L$-Functions, World Sci. Publ. Hackensack. NJ

      Pages: 219-370

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Volume of truncated fundamental domains.2007

    • Author(s)
      翁 林
    • Journal Title

      Proc. Amer. Math. Soc. 135

      Pages: 1681-1688

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Rigid Geometry and Applications2007

    • Author(s)
      加藤 文元
    • Journal Title

      Advanced Studies in Pure Mathematics 45

      Pages: 325-384

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary 2006 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rigid analytic geometry2007

    • Author(s)
      加藤 文元
    • Journal Title

      Sugaku Expositions. 20

      Pages: 65-95

    • NAID

      10013701820

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] The moduli space of 5 points on P1 and K3 surfaces.2007

    • Author(s)
      金銅 誠之
    • Journal Title

      Progr. In Math., Birkhauser 260

      Pages: 189-206

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Moduli of K3 surfaces and complex ball quotients2007

    • Author(s)
      金銅 誠之
    • Journal Title

      Progr. In Math., Birkhauser 260

      Pages: 43-100

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] The moduli space of 8 points of $\Bbb P\sp 1$ and automorphic forms2007

    • Author(s)
      金銅 誠之
    • Journal Title

      Contemp. Math., Amer. Math. Soc. 422

      Pages: 89-106

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Invariant functions with respect to the Whitehead-Link.2007

    • Author(s)
      松本圭司
    • Journal Title

      Progr. Math., 260, Birkhauser 260

      Pages: 245-271

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Dominant rational maps in the category of log schemes2007

    • Author(s)
      森脇 淳
    • Journal Title

      Tohoku Math. J. 59

      Pages: 481-525

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Moduli of vector bundles on algebraic surfaces2007

    • Author(s)
      吉岡 康太
    • Journal Title

      Sugaku Expositions 20

      Pages: 225-247

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Instanton counting and Donaldson invariants2007

    • Author(s)
      吉岡 康太, 中島 啓
    • Journal Title

      Sugaku (Japanese) 59

      Pages: 131-153

    • NAID

      10019542192

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] A geometric approach to L-function2007

    • Author(s)
      Ling Weng
    • Journal Title

      The Conference on $L$-Functions (World Sci. Publ.)

      Pages: 219-370

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Volume of truncated fundamental domains2007

    • Author(s)
      Ling Weng
    • Journal Title

      Proc. Amer. Math. Soc. Vol.135

      Pages: 1681-1688

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Rigid Geometry and Applications2007

    • Author(s)
      Fumiharu Kato
    • Journal Title

      Advanced Studies in Pure Mathematics Vol.45

      Pages: 325-384

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Rigid analytic geometry2007

    • Author(s)
      Fumiharu Kato
    • Journal Title

      Sugaku Expositions Vol.20

      Pages: 65-95

    • NAID

      10013701820

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] The moduli space of 5 points on P1and K3 surfaces2007

    • Author(s)
      Shigeyuki Kondo
    • Journal Title

      Progr. in Math. (Birkhauser) Vol.260

      Pages: 189-206

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Moduli of K3 surfaces and complex ball quotients2007

    • Author(s)
      Shigeyuki Kondo
    • Journal Title

      Progr. in Math. (Birkhauser) Vol.260

      Pages: 43-100

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] The moduli space of 8 points of P1 and automorphic forms2007

    • Author(s)
      Shigeyuki Kondo
    • Journal Title

      Contempt. Math., Amer. Math. Soc. Vol.422

      Pages: 89-106

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Invariant functions with respect to the Whitehead-Link2007

    • Author(s)
      Keiji Matsumoto
    • Journal Title

      Progr. in Math. (Birkhauser) Vol.260

      Pages: 245-271

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Dominant rational maps in the category of log schemes2007

    • Author(s)
      Atsushi Moriwaki
    • Journal Title

      Tohoku Math. J. Vol.59

      Pages: 481-525

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Moduli of vector bundles on algebraic surfaces2007

    • Author(s)
      Kota Yoshioka
    • Journal Title

      Sugaku Expositions Vol.20

      Pages: 225-247

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Instanton counting and Donaldson invariants2007

    • Author(s)
      Kota Yoshioka, Hikaru Nakajima
    • Journal Title

      Sugaku (Japanese) Vol.59

      Pages: 131-153

    • NAID

      10019542192

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] A geometric approach to L-functions2007

    • Author(s)
      翁 林
    • Journal Title

      The Conference on $L$-Functions, Worls Sci. Publ., Hackensack, NJ

      Pages: 219-370

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Instanton counting and Donaldson invariants2007

    • Author(s)
      吉岡 康太, 中島 啓
    • Journal Title

      Sugaku(Japanese) 59

      Pages: 131-153

    • NAID

      10019542192

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Geometric Approach to L-Functions2007

    • Author(s)
      翁 林
    • Journal Title

      Conference on L-Functions (World Scientific)

      Pages: 219-370

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Moduli of K3 surfaces and complex ball quotients2007

    • Author(s)
      金銅 誠之
    • Journal Title

      Progress in Mathematics 260

      Pages: 43-100

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The moduli space of 5 points on P^1 and K3 surfaces2007

    • Author(s)
      金銅 誠之
    • Journal Title

      Progress in Mathematics 260

      Pages: 189-206

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The moduli space of 8 points on P^1 and automorphic forms2007

    • Author(s)
      金銅 誠之
    • Journal Title

      Contemporary Mathematics 422

      Pages: 89-106

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The cohomology groups of stable quasi-abelian schemes and degenerations associated with the E8-lattice2006

    • Author(s)
      中村 郁
    • Journal Title

      Adv. Stud. Pure Math. 45

      Pages: 223-281

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] The cohomology groups of stable quasi-abelian schemes and degenerations associated with the E8-lattice2006

    • Author(s)
      Iku Nakamura
    • Journal Title

      Adv. Stud. Pure Math. Vol.45

      Pages: 223-281

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] The cohomology groups of stable quasi-abelian schemes and degenerations associated with the $E_8$-lattice, Moduli Spaces and Arithmetic Geometry2006

    • Author(s)
      中村 郁
    • Journal Title

      Advanced Studies in Pure Mathematics 45

      Pages: 221-279

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Rank two zeta and its zeros2006

    • Author(s)
      翁 林
    • Journal Title

      J. Ramanujan Math Soc. 21 No. 3

      Pages: 205-206

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Automorphic Forms, Eisenstein series and Spectral decompositions2006

    • Author(s)
      翁 林
    • Journal Title

      Arithmetic Geometry and Number Theory (World Scientific)

      Pages: 123-210

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Arithmetic structure of CMSZ fake projective plane2006

    • Author(s)
      加藤 文元
    • Journal Title

      Journal of Algebra 305

      Pages: 1166-1185

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Floer-Novikov cohomology and the flux conjecture2006

    • Author(s)
      小野 薫
    • Journal Title

      Geometric and Functional Analysis 16

      Pages: 981-1020

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Development in symplectic Floer theory2006

    • Author(s)
      小野 薫
    • Journal Title

      Proceedings of the International Congress of Mathematicians (EuroPean Mathematical Society) 2

      Pages: 1061-1082

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Algebraic relations among theta functions on the bounded symmetric domain of type $I_{r, r}$2006

    • Author(s)
      松本 圭司
    • Journal Title

      Kyushu J. Math 60

      Pages: 63-77

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Automorphic functions with respect to the fundamental group of thecomplement of the Borromean rings2006

    • Author(s)
      松本 圭司
    • Journal Title

      J. Math. Sci. Univ. Tokyo 13

      Pages: 1-11

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Maximal subgroups of the mathieu group M_{23} and symplectic automprohisms of supersingular K3 surfaces2006

    • Author(s)
      金銅 誠之
    • Journal Title

      International Mathematics Research Notices

      Pages: 1-9

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Non-abelian zeta functions for function fields.2005

    • Author(s)
      翁 林
    • Journal Title

      Amer. J. Math. 127 No.5

      Pages: 973-1017

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Simple singularities and symplectic fillings2005

    • Author(s)
      小野 薫
    • Journal Title

      J. Differential Geom. 69

      Pages: 1-42

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Symplectic 4-manifolds contaning singular rational curves with (2,3)-cusp2005

    • Author(s)
      小野 薫
    • Journal Title

      Seminaire et Congres 10

      Pages: 233-241

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A short note on symplectic Floer theory2005

    • Author(s)
      小野 薫
    • Journal Title

      Noncommutative Geometry and Physics

      Pages: 301-319

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A complex ball uniformization of the moduli space of cubic surfaces via periods of K3 surfaces2005

    • Author(s)
      金銅 誠之
    • Journal Title

      J. reine angew. Math. 588

      Pages: 99-148

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Isotropy representation for Harish-Chandra modules2005

    • Author(s)
      山下 博
    • Journal Title

      Infinite Dimensional Harmonic Analysis III

      Pages: 325-351

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Planar cubic curves, from Hesse to Mumford2004

    • Author(s)
      中村 郁
    • Journal Title

      Sugaku Expositions 17

      Pages: 73-101

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Coinvariant algebras of finite subgroups of SL(3,C)2004

    • Author(s)
      中村 郁
    • Journal Title

      Canad. J. Math. 56

      Pages: 495-528

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Planar cubic curves, from Hesse to Mumford2004

    • Author(s)
      Iku Nakamura
    • Journal Title

      Sugaku Expositions Vol.17

      Pages: 73-101

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Coinvariant algebras of finite subgroups of SL(3,C)2004

    • Author(s)
      Iku Nakamura
    • Journal Title

      Canad. J. Math Vol.56

      Pages: 495-528

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Planar cubic curves -- from Hesse to Mumford2004

    • Author(s)
      I.Nakamura
    • Journal Title

      Sugaku Expositions, Amer.Math.Soc. 17

      Pages: 73-101

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Coinvariant algebras of finite subgroups in SL(3,C)2004

    • Author(s)
      I.Nakamura
    • Journal Title

      Canadian Jour.Math. 56

      Pages: 495-528

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Numerical characterisations of hyperquadrics2004

    • Author(s)
      Y.Miyaoka
    • Journal Title

      Adv.Stud.Pure Math. (Complex analysis in several variables - Memorial Conference of Kiyoshi Oka's Centennial Birthday) 42

      Pages: 209-235

    • Related Report
      2004 Annual Research Report
  • [Journal Article] L^2-metrics, projective flatness of polarized abelian varieties2004

    • Author(s)
      Weng, Lin
    • Journal Title

      Trans.Amer.Math.Soc. 356,no.7

      Pages: 2685-2707

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Lectures on instanton counting2004

    • Author(s)
      K.Yoshioka
    • Journal Title

      CRM Proceedings & Lecture Notes, Proceedings of "Workshop on algebraic structures and moduli spaces", July 14 - 20, 2003, Centre de recherches mathematiques, Universite de Montreal 38

      Pages: 31-101

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Non-abelian zeta functions for function fields

    • Author(s)
      Weng, Lin
    • Journal Title

      Amer.J.Math. (to appear)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A complex ball uniformization of the moduli space of cubic surfaces

    • Author(s)
      S.Kondo
    • Journal Title

      J.reine angew.Math. (to appear)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Completion of real fans and Zariski-Riemann spaces

    • Author(s)
      M.Ishida
    • Journal Title

      Tohoku Math.J. (to appear)

    • NAID

      110004669750

    • Related Report
      2004 Annual Research Report
  • [Presentation] Tropical toric geometry2007

    • Author(s)
      梶原健
    • Organizer
      城崎代数幾何学シンポジウム
    • Place of Presentation
      兵庫県城崎大会議場
    • Year and Date
      2007-10-23
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Tropical toric geometry2007

    • Author(s)
      Takeshi Kajikawa
    • Organizer
      Kinosaki Algebraic Geometry Symposium
    • Place of Presentation
      Kinosaki Conference Hall, Hyogo
    • Year and Date
      2007-10-23
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Brane tilings and moduli of quiver representations2007

    • Author(s)
      石井亮
    • Organizer
      高次元代数多様体とベクトル束の代数幾何学
    • Place of Presentation
      九州大学
    • Year and Date
      2007-09-12
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Brane tilings and moduli of quiver representations2007

    • Author(s)
      Akira Ishii
    • Organizer
      Algebraic geometry of higher-dimensional algebraic varieties and vector bundles
    • Place of Presentation
      Kyushu University
    • Year and Date
      2007-09-12
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 分割表の一致率検定への有限群論と組合せ論の応用2007

    • Author(s)
      吉田知行
    • Organizer
      代数学シンポジウム
    • Place of Presentation
      神戸大学
    • Year and Date
      2007-08-17
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Application of finite group theory and combinatorics to inspection of coincidence probability in the partition table2007

    • Author(s)
      Yoshiyuki Yoshida
    • Organizer
      Algebraic Symposium
    • Place of Presentation
      Kobe University
    • Year and Date
      2007-08-17
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The moduli of plane quartics, Goepel invariants and Borcherds products2007

    • Author(s)
      金銅誠之
    • Organizer
      代数学シンポジウム
    • Place of Presentation
      神戸
    • Year and Date
      2007-08-08
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Arithmetic Hilbert-Samuel formula2007

    • Author(s)
      森脇 淳
    • Organizer
      代数学シンポジウム
    • Place of Presentation
      神戸大学
    • Year and Date
      2007-08-08
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] The moduli of plane quartics2007

    • Author(s)
      Shigeyuki Kondo
    • Organizer
      Goepel invariants and Borcherds products algebraic Symposium
    • Place of Presentation
      Kobe
    • Year and Date
      2007-08-08
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Arithmetic Hilbert-Samuel formula2007

    • Author(s)
      Atsushi Moriwaki
    • Organizer
      Algebraic Symposium
    • Place of Presentation
      Kobe University
    • Year and Date
      2007-08-08
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The moduli of plane quartics2007

    • Author(s)
      金銅誠之
    • Organizer
      Goepel invariants and Borcherds products 代数学シンポジウム
    • Place of Presentation
      神戸
    • Year and Date
      2007-08-08
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the moduli of quiver representations associated with brane tilings2007

    • Author(s)
      石井亮
    • Organizer
      高次元代数多様体とベクトル束
    • Place of Presentation
      京大数理研
    • Year and Date
      2007-07-05
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] On the moduli of quiver representations associated with brane tilings2007

    • Author(s)
      Akira Ishii
    • Organizer
      Higher-dimensional algebraic varieties and vector bundles
    • Place of Presentation
      RIMS, Kyoto University
    • Year and Date
      2007-07-05
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The moduli of plane quartics and Borcherds products2007

    • Author(s)
      金銅誠之
    • Organizer
      Modular forms and Moduli spaces, Satellite meeting for festival dedicated to 300th birthday of Leonhard Euler
    • Place of Presentation
      Saint-Petersburg (ロシア)
    • Year and Date
      2007-07-04
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The moduli of plane quartics and Borcherds products2007

    • Author(s)
      Shigeyuki Kondo
    • Organizer
      Modular forms and Moduli spaces, Satellite meeting for festival dedicated to 300^<th> birthday of Leonhard Euler
    • Place of Presentation
      Saint-Petersburg, Russia
    • Year and Date
      2007-07-04
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The moduli of plane quartics and Borcherds products2007

    • Author(s)
      金銅誠之
    • Organizer
      Modular forms and Moduli spaces, Satellite meeting for festival dedicated to 300th birthday of Leonhard Euler
    • Place of Presentation
      Saint-Petersburg(ロシア)
    • Year and Date
      2007-07-04
    • Related Report
      2007 Annual Research Report
  • [Presentation] The G-orbit Hilbert schemes and McKay correspondence for simple Singularities2007

    • Author(s)
      中村 郁
    • Organizer
      国際研究集会(Conference in honor of John McKay)"Groups and Symmetries: from the Neolithic Scots to John McKay"
    • Place of Presentation
      Centre de recherches mathematiques (University of Montreal)
    • Year and Date
      2007-04-28
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The G-orbit Hilbert schemes and McKay correspondence for simple singularities2007

    • Author(s)
      Iku Nakamura
    • Organizer
      International Conference (Conference in honor of John McKay) "Groups and Symmetries: from the Neolithic Scots to John McKay)
    • Place of Presentation
      Centre de recherches mathematiques (University of Montreal)
    • Year and Date
      2007-04-28
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The G-orbit Hilbert schemes and McKay correspondence for simple Singularities2007

    • Author(s)
      中村 郁
    • Organizer
      国際研究集会(Conference in honor of John McKay)"Groups and Symmetries: from the Neolithic Scots to John McKay"
    • Place of Presentation
      Centre de recherches mathematiques(University of Montreal)
    • Year and Date
      2007-04-28
    • Related Report
      2007 Annual Research Report
  • [Presentation] トロピカル幾何と代数幾何2007

    • Author(s)
      梶原健
    • Organizer
      日本数学会春季代数学分科会 (特別講演)
    • Place of Presentation
      埼玉大学
    • Year and Date
      2007-03-27
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Tropical geometry and algebraic geometry2007

    • Author(s)
      Takeshi Kajikawa
    • Organizer
      Mathematical Society of Japan, Spring Meeting Algebra Section
    • Place of Presentation
      Saitama University (Invited Lecture)
    • Year and Date
      2007-03-27
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] トロピカル幾何学について2007

    • Author(s)
      梶原健
    • Organizer
      計算可換代数と計算代数幾何
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-01-17
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On tropical geometry2007

    • Author(s)
      Takeshi Kajikawa
    • Organizer
      Computational commutative algebra and computational algebraic geometry
    • Place of Presentation
      RIMS, Kyoto University
    • Year and Date
      2007-01-17
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Floer thoery for Lagrangian submanifolds and an analog of the flux Conjecture for Lagrangian submanifolds2007

    • Author(s)
      小野薫
    • Organizer
      Gokova Geometry-Topology Conference
    • Place of Presentation
      Gokova, Turkey
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Floer-Novikov cohomology and symplectic fixed points2007

    • Author(s)
      小野薫
    • Organizer
      Postnikov Memorial Conference, Algebraic Topology
    • Place of Presentation
      Old and New Bedlewo Conference Center, Poland
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Floer-Novikov cohomology and symplectic fixed points2007

    • Author(s)
      小野薫
    • Organizer
      AMS-IMS-SIAM Joint Summer Institute "Symplectic topology and measure preserving dynamical systems" invariants"
    • Place of Presentation
      Snowbird, U.S.A.
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] An analogous question to the flux conjecture for Lagrangian submanifolds2007

    • Author(s)
      小野薫
    • Organizer
      Symplectic Geometry
    • Place of Presentation
      ETH Zurich, Switzerland
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Floer theory for Lagrangian submanifolds and an analog of the flux Conjective for Lagrangian submanifolds2007

    • Author(s)
      Kaoru Ono
    • Organizer
      Gokova Geometry-Topology Conference
    • Place of Presentation
      Gokova, Turkey
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Floer-Novikov cohomology and symplectic fixed points2007

    • Author(s)
      Kaoru Ono
    • Organizer
      AMS-IMS-SIAM Joint Summer Institute "Symplectic topology and measure preserving dynamical systems"
    • Place of Presentation
      Snowbird, U.S.A
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Floer thoery for Lagrangian submanifolds and an analog of the flux Conjecture for Lagrangian submanifolds2007

    • Author(s)
      小野薫
    • Organizer
      Gokova Geometry-Topology Conference
    • Place of Presentation
      Gokove, Turkey
    • Related Report
      2007 Annual Research Report
  • [Presentation] Floer-Novikov cohomology and symplectic fixed points2007

    • Author(s)
      小野薫
    • Organizer
      AMS-IMS-SIAM Joint Summer Institute "Symplectic topology and measure preserving dynamical systems"
    • Place of Presentation
      Snowbird, U. S. A.
    • Related Report
      2007 Annual Research Report
  • [Presentation] The Markov traces and Lusztig's Fourier transforms2006

    • Author(s)
      五味靖
    • Organizer
      2006年日本数学会年会代数分科会 (特別講演)
    • Place of Presentation
      中央大学
    • Year and Date
      2006-03-29
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The Markov traces and Lusztig's Fourier transforms2006

    • Author(s)
      Yasushi Gomi
    • Organizer
      Mathematical Society of Japan, Annual Meeting Algebra Section
    • Place of Presentation
      Chuo University, Mathematical Society of Japan (Invited Lecture)
    • Year and Date
      2006-03-29
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] 「数学する精神 - 正しさの創造, 美しさの発見」(中公新書 1912)2007

    • Author(s)
      加藤文元
    • Total Pages
      244
    • Publisher
      中央公論社
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] 線形代数学2007

    • Author(s)
      中村, 郁
    • Total Pages
      273
    • Publisher
      数学書房
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] Mathematical Minds - Creation of truth, discovery of beauty2007

    • Author(s)
      Fumiharu Kato
    • Total Pages
      244
    • Publisher
      Chuokoron-shinsha
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] Linear Algebra2007

    • Author(s)
      Iku Nakamura
    • Total Pages
      273
    • Publisher
      Sugakushobo
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] 「数学する精神-正しさの創造, 美しさの発見」(中公新書 1912)2007

    • Author(s)
      加藤文元
    • Total Pages
      244
    • Publisher
      中央公論社
    • Related Report
      2007 Annual Research Report
  • [Book] 線形代数学2007

    • Author(s)
      中村 郁
    • Total Pages
      273
    • Publisher
      数学書房
    • Related Report
      2007 Annual Research Report
  • [Book] Moduli Spaces and Arithmetic Geometry, Advanced Studies in Pure Mathematics vo1. 452007

    • Author(s)
      向井 茂
    • Total Pages
      370
    • Publisher
      Mathematical Society of Japan
    • Related Report
      2006 Annual Research Report
  • [Book] Arithmetic Geometry and Number Theory, Number Theory and Its Applications vol. 12006

    • Author(s)
      翁 林
    • Total Pages
      400
    • Publisher
      World Scientific
    • Related Report
      2006 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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