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Equivariant theory of Chern classes, Integrals based on Euler characteristics and related topics

Research Project

Project/Area Number 17340013
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

OHMOTO Toru  Hokkaido University, 大学院・理学研究院, 准教授 (20264400)

Co-Investigator(Kenkyū-buntansha) 與倉 昭治  鹿児島大学, 理学部, 教授 (60182680)
諏訪 立雄  新潟大学, 自然科学系, 教授 (40109418)
石川 剛郎  北海道大学, 大学院・理学研究院, 教授 (50176161)
秋田 利之  北海道大学, 大学院・理学研究院, 准教授 (30279252)
Co-Investigator(Renkei-kenkyūsha) SHOJI Yokura  鹿児島大学, 理学部, 教授 (60182680)
TATSUO Suwa  北海道大学, 理学部, 名誉教授 (40109418)
GO-O Ishikawa  北海道大学, 大学院・理学研究院, 教授 (50176161)
TOSHIYUKI Akita  北海道大学, 大学院・理学研究院, 准教授 (30279252)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥5,760,000 (Direct Cost: ¥5,100,000、Indirect Cost: ¥660,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,800,000 (Direct Cost: ¥1,800,000)
Keywords特異点論 / 特性類 / 特異チャーン類 / トム多項式 / チャーン・マクファーソン自然変換 / 構成的関数 / 代数的スタック / 同変ホモロジー / 局所化公式 / シューベルト計算 / チャーン類 / オービフォルド
Research Abstract

研究代表者の同変特異チャーン類理論を基礎に, 種々のオビフォルド・特異チャーン類を定義した. 特に, 古典的群論における置換表現の数え上げ公式をオビフォルド特性類に拡張したものとして, 代数多様体の対称積に関するオビフォルド・特異チャーン類の生成母関数公式を示した. これは, 特異チャーン類理論の数え上げ幾何あるいはマッカイ対応への応用に向けた足場となる.

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (67 results)

All 2009 2008 2007 2006 2005 Other

All Journal Article (41 results) (of which Peer Reviewed: 29 results) Presentation (26 results)

  • [Journal Article] 特異点の数え上げと同変Chern類, 数学, 岩波書店2009

    • Author(s)
      大本亨
    • Journal Title

      日本数学会編 61巻1号

      Pages: 21-39

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] 特異点の数え上げと同変Chem類2009

    • Author(s)
      大本亨
    • Journal Title

      数学(日本数学会編, 岩波書店) 61

      Pages: 21-39

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Thom polynomials and around2009

    • Author(s)
      T. Ohmoto
    • Journal Title

      RIMS Koukyuroku Bessatsu 11

      Pages: 75-86

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generating functions of orbifold Chern classes I : Symmetric Products2008

    • Author(s)
      T. Ohmoto
    • Journal Title

      Math. Proc. Cambridge Phil. Soc. 144

      Pages: 423-438

    • Related Report
      2008 Annual Research Report 2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On mod p Riemann-Roch formulae for mapping class groups2008

    • Author(s)
      T. Akita
    • Journal Title

      Advanced Studies in Pure Math 52

      Pages: 111-118

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A formula for the Euler characteristics of even dimensional triangulated manifolds2008

    • Author(s)
      T. Akita
    • Journal Title

      Proc. Amer. Math. Soc. 136

      Pages: 2571-2573

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Integral Riemann-Roch formulae for cyclic subgroups of mapping class groups2008

    • Author(s)
      T. Akita, and Nariya Kawazumi
    • Journal Title

      Math. Proc. Cambridge Phil. Soc. 144

      Pages: 411-421

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcations in symplectic space2008

    • Author(s)
      G. Ishikawa, and S. Janeczko
    • Journal Title

      Banach Center Publ vol.82

      Pages: 111-124

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generic singularities of implicit systems of first order differential equations on the plane2008

    • Author(s)
      A. A. Davydov, G. Ishikawa, S. Izumiya, W.-Z. Sun
    • Journal Title

      Japanese Journal of Math. ematics vol.3-1

      Pages: 93-119

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global classification of curves on the symplectic plane, Proceedings of the IX Workshop on Real and Complex Singularities2008

    • Author(s)
      G. Ishikawa
    • Journal Title

      Sao Carlos, 2006, Contemp.Math. 459, Amer. Math. Soc.

      Pages: 51-72

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] 特異点の数え上げと同変Chern類2008

    • Author(s)
      大本 亨
    • Journal Title

      数学(日本数学会)(to appear) 60・未定

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Grothendieck transformations in Fulton-MacPherson's bivariant theory2008

    • Author(s)
      S. Yokura
    • Journal Title

      Journal of Pure and Applied Algebra 211・未定

      Pages: 665-684

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global classification of curves on the symplectic plane2008

    • Author(s)
      G. Ishikawa
    • Journal Title

      Proc. IX Workshop on Real and Complex Singularities (Sao Carlos, 2006) Contemporary Mathematics, AMS (to appear)

    • NAID

      120006459528

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Zariski's moduli problem for plane branches and the classification of Legendre curve singularities2008

    • Author(s)
      G. Ishikawa
    • Journal Title

      Proceedings of the Australian-Japanese Workshop(Univ. Sydney, Australia 5-8 Sep. 2005).World Scientific

      Pages: 56-84

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On mod p Riemann-Roch formulae for mapping class groups2008

    • Author(s)
      T. Akita
    • Journal Title

      Advanced Studies in Pure Math.(to appear)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integral Riemann-Roch formulae for cyclic subgrougs of mapping class groups2008

    • Author(s)
      T. Akita
    • Journal Title

      Math. Proc. Cambridge Phil. Soc.(to appear)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Residue Theoretical Approach to Intersection Theory2008

    • Author(s)
      T. Suwa
    • Journal Title

      Proceedings of IX Workshop on Real and Complex Singularities, Sao Carlos, Brazil, Contemporary Math., AMS.(55 pages). (to appear)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generating functions of orbifold Chern classes I : symmetric products2008

    • Author(s)
      T.Ohmoto
    • Journal Title

      Math. Proc. Cambridge Phil. Soc. (to appear)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Chern classes and Thom polynomials2007

    • Author(s)
      T. Ohmoto
    • Journal Title

      Proc. Trieste Singularity Summer School and Workshop (ICTP, Trieste, 2005) ed. J-P. Brasselet et.al., World Scientific

      Pages: 464-482

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Introduction to Complex Analytic Geometry2007

    • Author(s)
      T. Suwa
    • Journal Title

      Proc. Trieste Singularity Summer School and Workshop (ICTP, Trieste, 2005) ed. J-P.Brasselet et.al., World Scientific

      Pages: 161-222

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Chern classes and Thom polynomials2007

    • Author(s)
      T. Ohmoto
    • Journal Title

      Singularities in geometry and topolopy, World Sci.Publ. Hackensack, NJ

      Pages: 464-482

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the uniquness of bivariant Chern classes and bivariant Riemann-Roch transformations2007

    • Author(s)
      S. Yokura
    • Journal Title

      Advances in Mathematics 210・2

      Pages: 797-812

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Introduction to complex analytic geometry2007

    • Author(s)
      T. Suwa
    • Journal Title

      Singularities in geometry and topology, World Sci. Publ. Hackensank, NJ

      Pages: 161-220

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Chern classes and Thom polynomials2007

    • Author(s)
      T.Ohmoto
    • Journal Title

      Proc. Trieste Singularity Summer School and Workshop (ICTP, Trieste, 2005) (ed. J-P.Brasselet et al) (World Scientific)

      Pages: 464-482

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Introduction to Complex Analytic Geometry2007

    • Author(s)
      T.Suwa
    • Journal Title

      Proc. Trieste Singularity Summer School and Workshop (ICTP, Trieste, 2005) (ed. J-P. Brasselet et al) (World Scientific)

      Pages: 161-222

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A formula for the Euler characteristics of even dimensional triangulated manifolds2007

    • Author(s)
      T.Akita
    • Journal Title

      Proc. Amer. Math. Soc. (to appear)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Equivariant Chern classes of singular algebraic varieties with group actions2006

    • Author(s)
      T. Ohmoto
    • Journal Title

      Math. Proc. Cambridge Phil. Soc. 140

      Pages: 115-134

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Classe de Hirzebruch et classes de Chern motiviques2006

    • Author(s)
      J-P. Brasselet, J. Shurmann S. Yokura
    • Journal Title

      C. R. Math. Acad. Sci. Paris 342-5

      Pages: 325-328

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Singularities of improper affine spheres and surfaces of constant Gaussian curvature2006

    • Author(s)
      G.Ishikawa
    • Journal Title

      Internat. Jour. Math. 17・3

      Pages: 269-293

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Classe de Hirzebruch et classes de Chern motiviques2006

    • Author(s)
      S.Yokura
    • Journal Title

      C. R. Math. Acad. Sci. Paris 342・5

      Pages: 325-328

    • Related Report
      2006 Annual Research Report
  • [Journal Article] First order local invariants of apparent contours2006

    • Author(s)
      T.Ohmoto
    • Journal Title

      Topology 45

      Pages: 27-45

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Equivariant Chern classes of singular algebraic varieties with group actions2006

    • Author(s)
      T.Ohmoto
    • Journal Title

      Mathematical proceedings of the Cambridge Philosophical Society / Cambridge Philosophical Society 140

      Pages: 115-134

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Residues for holomorphic foliations of singular pairs2005

    • Author(s)
      T. Suwa
    • Journal Title

      Advances in Geometry 5

      Pages: 81-95

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generalized Ginzburg Chern classes, Singularites Franco-Japonaises2005

    • Author(s)
      S. Yokur, a
    • Journal Title

      Semin. Congr. 10, Soc. Math. France 34

      Pages: 429-442

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bivariant Chern classes for morphisms with nonsingular target varieties2005

    • Author(s)
      S.Yokura
    • Journal Title

      Central European Journal of Mathematics 3

      Pages: 429-442

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Generalized Ginzburg-Chern classes2005

    • Author(s)
      S.Yokura
    • Journal Title

      Singularites Franco-Japonaises, Semin.Congr.10,Soc.Math.France, Paris, 3・4

      Pages: 429-442

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Residues for holomorphic foliations of singular pairs2005

    • Author(s)
      T.Suwa
    • Journal Title

      Advances in Geometry 5

      Pages: 81-95

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Infinitesimal deformations and stability of singular Legendre submanifolds2005

    • Author(s)
      G.Ishikawa
    • Journal Title

      Asian Journal of Mathematics 9・1

      Pages: 133-166

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Oriented bivariant theories, I

    • Author(s)
      S. Yokura
    • Journal Title

      International Journal of Mathematics (掲載決定)

      Pages: 30-30

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A universal bivariant theory and cobordism groups

    • Author(s)
      S. Yokura
    • Journal Title

      Advanced Studies in Pure Mathemaics (掲載決定)

      Pages: 31-31

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Motivic characteristic classes

    • Author(s)
      S. Yokura
    • Journal Title

      Proceedings of MSRI Workshop "Topology of Stratified Spaces"(MSRI Publications) (掲載決定)(arXiv:0812.4584v1 [math.AG])

      Pages: 32-32

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Presentation] Surface symmetries and group cohomology2008

    • Author(s)
      T. Akita
    • Organizer
      福岡微分幾何研究会
    • Place of Presentation
      福岡大学セミナーハウス
    • Year and Date
      2008-11-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Generating function of Chernclasses of Hilbert schemes of points2008

    • Author(s)
      T. Ohmoto
    • Organizer
      特異点と多様体の幾何-草津2008-
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2008-09-12
    • Related Report
      2008 Final Research Report
  • [Presentation] Generating function of Chern classes of Hilbert schemes of points2008

    • Author(s)
      T. Ohmoto
    • Organizer
      特異点と多様体の幾何-草津2008-
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2008-09-12
    • Related Report
      2008 Annual Research Report
  • [Presentation] Motivic characteristic classes of singluar varieties2008

    • Author(s)
      S. Yokura
    • Organizer
      Workshop Topology of Stratified Spaces
    • Place of Presentation
      MSRI, UC. Berkeley
    • Year and Date
      2008-09-11
    • Related Report
      2008 Final Research Report
  • [Presentation] Local symplectic invariants of parametric Lagrangian varieties2008

    • Author(s)
      G. Ishikawa
    • Organizer
      Frobenius structures and singularity theory
    • Place of Presentation
      Bedlewo, Poland
    • Year and Date
      2008-08-26
    • Related Report
      2008 Final Research Report
  • [Presentation] Classification of parametric varieties in the symplectic space:Motivations, Examples and Problems2008

    • Author(s)
      G. Ishikawa
    • Organizer
      10th International Workshop on Real and Compex Singularities
    • Place of Presentation
      Sao Carlos, Brazil
    • Year and Date
      2008-07-31
    • Related Report
      2008 Final Research Report
  • [Presentation] Equivariant Chow groups and Chern classes2008

    • Author(s)
      T. Ohmoto
    • Organizer
      研究集会「シューベルトカリキュラスとその周辺」
    • Place of Presentation
      関西セミナーハウス
    • Year and Date
      2008-03-18
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Thom polynomials and around I, II2008

    • Author(s)
      T. Ohmoto
    • Organizer
      接触幾何とその関連分野
    • Place of Presentation
      金沢大学サテライトプラザ
    • Year and Date
      2008-01-24
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Thom polynomials and around2007

    • Author(s)
      T. Ohmoto
    • Organizer
      研究集会「組み合わせ論的表現論の拡がり」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-10-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Thom polynomials and around2007

    • Author(s)
      T. Ohmoto
    • Organizer
      研究集会「組み合わせ論的表現諭の拡がり」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-10-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Surface symmetry, homology representations and group cohomology2007

    • Author(s)
      T. Akita
    • Organizer
      Algebras, Groups and Geometries in Tambara
    • Place of Presentation
      東大玉原国際セミナーハウス
    • Year and Date
      2007-10-17
    • Related Report
      2008 Final Research Report
  • [Presentation] Surface symmetry, homology representations and group cohomology2007

    • Author(s)
      T. Akita
    • Organizer
      Algebras, Groups and Geometries in Tambara
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2007-10-17
    • Related Report
      2007 Annual Research Report
  • [Presentation] Localization of Atiyah classes2007

    • Author(s)
      T. Suwa
    • Organizer
      Seminario di Analisi Complessa
    • Place of Presentation
      Universita di Roma Tor Vergata, Italy
    • Year and Date
      2007-10-02
    • Related Report
      2008 Final Research Report
  • [Presentation] Localization of Atiyah classes2007

    • Author(s)
      T. Suwa
    • Organizer
      Seminario di Analisi Complessa
    • Place of Presentation
      Universita di Roma "Tor Vergata", Italy
    • Year and Date
      2007-10-02
    • Related Report
      2007 Annual Research Report
  • [Presentation] 曲面上の群作用と群のコホモロジー2007

    • Author(s)
      T. Akita
    • Organizer
      研究集会「有限群のコホモロジー論とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-08-30
    • Related Report
      2008 Final Research Report
  • [Presentation] 曲面上の群作用と群のコホモロジー2007

    • Author(s)
      T. Akita
    • Organizer
      研究集会 「有限群のコホモロジー論とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-08-30
    • Related Report
      2007 Annual Research Report
  • [Presentation] Computing Milnor numbers via Thom polynomials2007

    • Author(s)
      T. Ohmoto
    • Organizer
      Niigata Workshop on Complex Geometry and Singularities
    • Place of Presentation
      クロスパル新潟
    • Year and Date
      2007-08-20
    • Related Report
      2008 Final Research Report
  • [Presentation] Localization of Atiyah classes2007

    • Author(s)
      T. Suwa
    • Organizer
      Niigata Workshop on Complex Geometry and Singularities
    • Place of Presentation
      クロスパル新潟
    • Year and Date
      2007-08-20
    • Related Report
      2008 Final Research Report
  • [Presentation] Computing Milnor numbers via Thom polynomials2007

    • Author(s)
      T. Ohmoto
    • Organizer
      Niigata Workshop on Complex Geometry and Singularities,
    • Place of Presentation
      クロスパル新潟
    • Year and Date
      2007-08-20
    • Related Report
      2007 Annual Research Report
  • [Presentation] Localization of Atiyah classes2007

    • Author(s)
      T. Suwa
    • Organizer
      Niigata Workshop on Complex Geometry and Singularities,
    • Place of Presentation
      クロスパル新潟
    • Year and Date
      2007-08-20
    • Related Report
      2007 Annual Research Report
  • [Presentation] Local classification of parametric Lagrangian varieties2007

    • Author(s)
      G. Ishikawa
    • Organizer
      Internation Conference "Symplectic Geometry"
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-07-27
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Calssification problem in symplectic singularity theory2007

    • Author(s)
      G. Ishikawa
    • Organizer
      Banach Center Symposium "Geometric SingularityTheory" Polish-Japanese Working Days
    • Place of Presentation
      Sopot, Poland
    • Year and Date
      2007-07-09
    • Related Report
      2008 Final Research Report
  • [Presentation] Calssification problem in symplectic singularity theory2007

    • Author(s)
      G. Ishikawa
    • Organizer
      Banach Center Symposium "Geometric Singularity Theory" Polish-Japanese Working Days,
    • Place of Presentation
      Sopot, Poland.
    • Year and Date
      2007-07-09
    • Related Report
      2007 Annual Research Report
  • [Presentation] Thom polynomials for complete intersection singularities2006

    • Author(s)
      T. Ohmoto
    • Organizer
      日露複素解析幾何 : 「複素代数多様体上の解析と幾何」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2006-12-14
    • Related Report
      2008 Final Research Report
  • [Presentation] Chern classes and Thom polynomials--Enumerative geometry of singularities2005

    • Author(s)
      大本亨
    • Organizer
      代数幾何・城崎シンポジウム
    • Place of Presentation
      兵庫県立城崎大会議館
    • Year and Date
      2005-10-27
    • Related Report
      2008 Final Research Report
  • [Presentation] Chern classes and Thom polynomials2005

    • Author(s)
      T. Ohmoto
    • Organizer
      ICTP Advanced School and Workshop:Singularities in Geometry and Topology
    • Place of Presentation
      Trieste(Italy)
    • Year and Date
      2005-08-24
    • Related Report
      2008 Final Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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