• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Hyperplane arrangements and their applications

Research Project

Project/Area Number 17340011
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHokkaido University (2006-2008)
Tokyo Metropolitan University (2005)

Principal Investigator

TERAO Hiroaki  Hokkaido University, 大学院理学研究院, 教授 (90119058)

Co-Investigator(Kenkyū-buntansha) MARTIN Guest  首都大学東京, 都市教養学部・理工系, 教授 (10295470)
TOKUNAGA Hiroo  首都大学東京, 都市教養学部・理工系, 教授 (30211395)
NAKASHIMA Tooru  日本女子大学, 理学部, 教授 (20244410)
NAKAMURA Ken  首都大学東京, 都市教養学部・理工系, 教授 (80110849)
MATSUNO Kazuo  津田塾大学, 学芸学部, 准教授 (40332936)
SAITO Kyoji  数物連携宇宙研究機構(IPMP), 主任研究員 (20012445)
TAKEMURA Akimichi  東京大学, 大学院情報理工学系研究科, 教授 (10171670)
TERASOMA Tomohide  東京大学, 大学院数理科学研究科, 教授 (50192654)
Co-Investigator(Renkei-kenkyūsha) MARTIN Guest  首都大学東京, 都市教養学部・理工系, 教授 (10295470)
TOKUNAGA Hiroo  首都大学東京, 都市教養学部・理工系, 教授 (30211395)
NAKASHIMA Tooru  日本女子大学, 理学部, 教授 (20244410)
NAKAMURA Ken  首都大学東京, 都市教養学部・理工系, 教授 (80110849)
MATSUNO Kazuo  津田塾大学, 学芸学部, 准教授 (40332936)
SAITO Kyoji  数物連携宇宙研究機構(IPMP), 主任研究員 (20012445)
TAKEMURA Akimichi  東京大学, 大学院・情報理工学系研究科, 教授 (10171670)
TERASOMA Tomohide  東京大学, 大学院・数理科学研究科, 教授 (50192654)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥14,950,000 (Direct Cost: ¥13,000,000、Indirect Cost: ¥1,950,000)
Fiscal Year 2008: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2007: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2006: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2005: ¥3,400,000 (Direct Cost: ¥3,400,000)
Keywords超平面配置 / 超幾何積分 / 鏡映群 / 局所系コホモロジー / コクセター群 / 対数的微分型式 / 対数的微分 / 多重超平面配置
Research Abstract

多重配置の自由性におけるふたつの基盤的な定理を証明した. ひとつは, 多重超平面配置の自由性に関する「加除定理」であり, もうひとつは, 多重自由超平面配置における「Solomon-Teraoの定理の拡張」である(ともに, 阿部拓郎(京大・理)とMax Wakefield(US Naval Academy)との共著). これにより, 多重超平面配置の具体的に自由性を論ずることが初めて可能になり, 自由配置の本質的意味の理解に近づいた.

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

    (61 results)

All 2009 2008 2007 2006 2005 Other

All Journal Article (32 results) (of which Peer Reviewed: 20 results) Presentation (24 results) Book (3 results) Remarks (2 results)

  • [Journal Article] Totally free arrangements of hyperplanes2009

    • Author(s)
      Abe Takuro, Terao Hiroaki, Yoshinaga Masahiko
    • Journal Title

      Proc. Amer. Math. Soc. 137, no. 4

      Pages: 1405-1410

    • NAID

      120006459611

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Totally free arrangements2009

    • Author(s)
      T. Abe, et.al.
    • Journal Title

      Proc. Amer. Math. Soc. 137

      Pages: 1405-1410

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodicity ofhyperplane arrangements withintegral coefficients modulopositive integers2008

    • Author(s)
      Kamiya Hidehiko, Takemura, Akimichi, Terao, Hiroaki
    • Journal Title

      J. Algebraic Combin 27, no. 3

      Pages: 317-330

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Euler multiplicity and addition-deletion theorems for multiarrangements2008

    • Author(s)
      Abe, Takuro, Terao, Hiroaki, Wakefield, Max
    • Journal Title

      J. Lond. Math. Soc (2) 77, no.2

      Pages: 335-348

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A correction to : "Bases of the contact-orderfiltration of derivations of Coxeterarrangements"2008

    • Author(s)
      Terao, Hiroaki
    • Journal Title

      Proc. Amer. Math. Soc. MR2099414 Proc. Amer. Math. Soc 133, no.7, 136, no.7

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Euler multiplicity and addition?deletion theorems for multiarrangements2008

    • Author(s)
      T. Abe, et.al.
    • Journal Title

      J. London Math. Soc. 77

      Pages: 3345-3478

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A correction to "Bases of the contact-order filtration of derivations of Coxeter arrangements"2008

    • Author(s)
      H. Terao
    • Journal Title

      Proc. Amer. Math. Soc. 136

      Pages: 2639-2639

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodicity of hyperplane arrangements with integral coefficients modulo positive integers2008

    • Author(s)
      H. Kamiya, et.al.
    • Journal Title

      J. Alg. Combin. 27

      Pages: 317-330

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodicity of hyperplane arrangements with integral coefficients modulo positive integers2008

    • Author(s)
      H. Terao
    • Journal Title

      J. Alg. Combin (発表予定)

    • NAID

      120006459543

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Euler multiplicity and the addition-deletion theorems for multiarrangements2008

    • Author(s)
      H. Terao
    • Journal Title

      J. London Math. Soc (発表予定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The characteristic polynomial of a multiarrangement2007

    • Author(s)
      Abe, Takuro, Terao, Hiroaki, Wakefield, Max
    • Journal Title

      Adv. Math. 215, no. 2

      Pages: 825-838

    • NAID

      120006459522

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Chambers of arrangements of hyperplanes and Arrow's impossibility theorem2007

    • Author(s)
      Terao, Hiroaki
    • Journal Title

      Adv. Math. 214, no. 1

      Pages: 366-378

    • NAID

      120000955425

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Arrangements and hypergeometric integrals. Second edition. MSJ Memoirs2007

    • Author(s)
      Orlik, Peter, Terao, Hiroaki
    • Journal Title

      9. Mathematical Society of Japan, Tokyo

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Chambers of Arrangements of Hyperplanes and Arrow's Impossibility Theorem2007

    • Author(s)
      Hiroaki Terao
    • Journal Title

      Advances in Math 214

      Pages: 366-378

    • NAID

      120000955425

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The characteristic polynomial of a multiarrangement2007

    • Author(s)
      H. Terao
    • Journal Title

      Advances in Math 215

      Pages: 825-838

    • NAID

      120006459522

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Chambers of Arrangements of Hyperplanes and Arrow' s Impossibility Theorem.2007

    • Author(s)
      H.Terao
    • Journal Title

      Advances in Mathematics (印刷中)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Arrangements and ranking patterns2006

    • Author(s)
      Kamiya, Hidehiko, Orlik, Peter, Takemura, Akimichi, Terao, Hiroaki
    • Journal Title

      Ann. Comb. 10, no.2

      Pages: 219-235

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Arrangements and ranking patterns.2006

    • Author(s)
      H, Terao
    • Journal Title

      Ann. Comb. 10

      Pages: 219-235

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Two-dimensional versal $G$-covers and Cremona embeddings of finite groups.2006

    • Author(s)
      H.Tokunaga
    • Journal Title

      Kyushu J. Math. 60

      Pages: 439-456

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Error-correcting codes on projective bundles.2006

    • Author(s)
      T.Nakashima
    • Journal Title

      Finite Fields Appl. 12

      Pages: 222-231

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when the scale parameters are exponentially small.2006

    • Author(s)
      A.Takemura
    • Journal Title

      Bernoulli 12

      Pages: 1003-1017

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Some improvements in numerical evaluation of symmetric stable density and its derivatives.2006

    • Author(s)
      A.Takemura
    • Journal Title

      Comm. Statist. Theory Methods 35

      Pages: 149-172

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The Hodge filtration and the contact-order filtration of derivations of Coxeter arrangements2005

    • Author(s)
      Terao, Hiroaki
    • Journal Title

      Manuscripta Math 118, no. 1

      Pages: 1-9

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bases of the contact-order filtration of derivations of Coxeter arrangements2005

    • Author(s)
      Terao, Hiroaki
    • Journal Title

      Proc. Amer. Math. Soc 133, no.7

      Pages: 2029-2034

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bases of the contact-order filtration of derivations of Coxeter arrangements.2005

    • Author(s)
      H.Terao
    • Journal Title

      Proc.AMS 133

      Pages: 2029-2034

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Quantum cohomology via D-modules2005

    • Author(s)
      M.Guest
    • Journal Title

      Topology 44

      Pages: 263-281

    • Related Report
      2005 Annual Research Report
  • [Journal Article] $2$-dimensional versal $S_4$-covers and rational elliptic surfaces2005

    • Author(s)
      H.Tokunaga
    • Journal Title

      Seminaire et Congres (Societe Mathematique de France) 10

      Pages: 307-322

    • Related Report
      2005 Annual Research Report
  • [Journal Article] ニュートン図形の極限同定と複素超曲面の特異点解消.2005

    • Author(s)
      小林正典, 徳永浩雄, 山本章博
    • Journal Title

      人工知能基本問題研究会資料SIG-FPAI-A403(2005)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Codes on Grassmann bundles and related varieties2005

    • Author(s)
      T.Nakashima
    • Journal Title

      J.Pure and Appl.Alg. 199

      Pages: 235-244

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Periodicity of non-central integral arrangements modulo positive integers

    • Author(s)
      H. Kamiya, et.al.
    • Journal Title

      Annals of Combinatorics (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A primitive derivation and logarithmic differential forms of Coxeter arrangements

    • Author(s)
      T. Abe, et.al.
    • Journal Title

      Math. Z. (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Arrangements and Ranking Patterns.

    • Author(s)
      H.Kamiya, P.Orlik, A.Takemura, H.Terao
    • Journal Title

      Annals of Combinatorics (印刷中)

    • Related Report
      2005 Annual Research Report
  • [Presentation] Periodicity ofhyperplane arrangements withintegral coefficients modulopositive integers2009

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Finite Groups,vertex operator algebras andcombinatorics
    • Place of Presentation
      RIMS, Kyoto University
    • Year and Date
      2009-01-06
    • Related Report
      2008 Final Research Report
  • [Presentation] Periodicity of hyperplane arrangements with integral coefficients modulo positive integers2009

    • Author(s)
      寺尾宏明
    • Organizer
      有限群, 頂点作用素と組合せ論
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-01-06
    • Related Report
      2008 Annual Research Report
  • [Presentation] Totally free arrangements of hyperplanes2008

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Conference in Honour of Peter Orlik
    • Place of Presentation
      Fields Institute, Toronto, Canada
    • Year and Date
      2008-08-19
    • Related Report
      2008 Final Research Report
  • [Presentation] Totally free arrangements of hyperplanes2008

    • Author(s)
      寺尾宏明
    • Organizer
      Conference on arrangements of hyperplanes
    • Place of Presentation
      フィールズ研究所(カナダ・トロント市)
    • Year and Date
      2008-08-19
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the free multiarrangements2008

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Millican Lecture, Colloquium
    • Place of Presentation
      University of North Texas
    • Year and Date
      2008-05-02
    • Related Report
      2008 Final Research Report
  • [Presentation] On the free multiarrangements2008

    • Author(s)
      H. Terao
    • Organizer
      Millican Lecture Series
    • Place of Presentation
      Univ. of North Texas(米国・テキサス州)
    • Year and Date
      2008-05-02
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the free multiarrangements, Several Aspects of Hyperplane Arrangements2008

    • Author(s)
      Terao, Hiroaki
    • Organizer
      1037TH American Mathematical Society Meeting, special session on Arrangements and Related Topics
    • Place of Presentation
      Louisiana State University, Baton Rouge, LA, USA
    • Year and Date
      2008-03-28
    • Related Report
      2008 Final Research Report
  • [Presentation] Periodicity of integral arrangements modulo positive integers2008

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Several Aspects of Hyperplane Arrangements
    • Place of Presentation
      Kobe, Japan
    • Year and Date
      2008-02-04
    • Related Report
      2008 Final Research Report
  • [Presentation] The characteristic quasi-polynomial of integral arrangements and root systems2007

    • Author(s)
      Terao, Hiroaki
    • Organizer
      CIMPAsummer school ALS \& S 2007, Arrangements and Local Systems
    • Place of Presentation
      Istanbul, Turkey
    • Year and Date
      2007-06-15
    • Related Report
      2008 Final Research Report
  • [Presentation] The characteristic polynomials of (multi) arrangements2007

    • Author(s)
      Terao, Hiroaki
    • Organizer
      CIMPA summer school ALS \& S 2007, Arrangements and Local Systems
    • Place of Presentation
      Istanbul, Turkey
    • Year and Date
      2007-06-15
    • Related Report
      2008 Final Research Report
  • [Presentation] The characteristic polynomials of (multi)arrangements2007

    • Author(s)
      寺尾 宏明
    • Organizer
      CIMPA summer school ALS & S 2007, Arrangements and Local Systems
    • Place of Presentation
      Istanbul, Turkey
    • Year and Date
      2007-06-15
    • Related Report
      2007 Annual Research Report
  • [Presentation] The characteristic quasi-polynomial of integral arrangements and root systems2007

    • Author(s)
      寺尾 宏明
    • Organizer
      CIMPA summer school ALS & S 2007, Arrangements and Local Systems
    • Place of Presentation
      Istanbul, Turkey
    • Year and Date
      2007-06-15
    • Related Report
      2007 Annual Research Report
  • [Presentation] Chambers of arrangements of hyperplanes andArrow's impossibility theorem,Braids and their Ramifications -Configuration Spaces, Arrangements2007

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Mapping, Mapping-Class groups, 3-Manifolds
    • Place of Presentation
      Cortona, Italy
    • Year and Date
      2007-05-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Chambers of arrangements of hyperplanes and Arrow's impossibility theorem2007

    • Author(s)
      寺尾 宏明
    • Organizer
      Braids and their Ramifications-Configuration Spaces, Arrangements, Mapping, Mapping-Class groups, 3-Manifolds
    • Place of Presentation
      Cortona, Italy
    • Year and Date
      2007-05-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] Chambers of arrangements of hyperplanes and Arrow's impossibility theorem2007

    • Author(s)
      Terao, Hiroaki
    • Organizer
      American Mathematical Society,Annual Meeting, special session onArrangements and Related Topics
    • Place of Presentation
      New Orleans Sheraton, New Orleans, LA, USA
    • Year and Date
      2007-01-06
    • Related Report
      2008 Final Research Report
  • [Presentation] Basic properties of multiarrangements, Geometry and analysis on complex varieties2006

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Research Institute for Mathematical Sciences (RIMS)
    • Place of Presentation
      Kyoto University
    • Year and Date
      2006-12-13
    • Related Report
      2008 Final Research Report
  • [Presentation] Chambers ofarrangements of hyperplanes andArrow's impossibility theorem2006

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Colloquium
    • Place of Presentation
      Okayama University
    • Year and Date
      2006-11-09
    • Related Report
      2008 Final Research Report
  • [Presentation] Chambers of arrangements of hyperplanes and Arrow's impossibility theorem2006

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Development of Computational Algebraic Statistics, ResearchInstitute for Mathematical Sciences (RIMS)
    • Place of Presentation
      Kyoto University
    • Year and Date
      2006-11-08
    • Related Report
      2008 Final Research Report
  • [Presentation] Multiderivations of Coxeter Arrangements of Type $B_\ell$ and Primitive Derivations2006

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Geometry and Analysis on Complex Algenbraic Varieties, Joint RFBR-JSPS Symposium
    • Place of Presentation
      Moscow Independent University
    • Year and Date
      2006-08-17
    • Related Report
      2008 Final Research Report
  • [Presentation] Multiderivations of real reflection arrangements2006

    • Author(s)
      Terao, Hiroaki
    • Organizer
      The international symposium on singularity theory and their applications II
    • Place of Presentation
      Beijing University of Chemical Technology, China
    • Year and Date
      2006-05-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Various phases of arrangements of hyperplanes2006

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Colloquium
    • Place of Presentation
      Hokkaido University
    • Year and Date
      2006-04-28
    • Related Report
      2008 Final Research Report
  • [Presentation] Multiderivations of Coxeter Arrangements of Type B_\ell and Primitive Derivations2006

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Colloquium
    • Place of Presentation
      Northern Arizona University
    • Year and Date
      2006-02-17
    • Related Report
      2008 Final Research Report
  • [Presentation] Introduction to hyperplane arrangements-Especially on free arrangements-Recent topics on real and complexsingularities2005

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Research Institute for Mathematical Sciences (RIMS)
    • Place of Presentation
      Kyoto University
    • Year and Date
      2005-11-28
    • Related Report
      2008 Final Research Report
  • [Presentation] What makes arrangements free? Euroconferences in Mathematics on Crete2005

    • Author(s)
      Terao, Hiroaki
    • Organizer
      Algebraicand Geometric Combinatorics
    • Place of Presentation
      Anogia, Greece
    • Year and Date
      2005-08-21
    • Related Report
      2008 Final Research Report
  • [Book] Arrangements and hypergeometric integrals(第2版)2007

    • Author(s)
      Hiroaki Terao
    • Total Pages
      121
    • Publisher
      MSJ Memoir, 9, Mathematical Society of Japan, Tokyo
    • Related Report
      2007 Annual Research Report
  • [Book] Integrable systems, geometry, and topology2006

    • Author(s)
      Martin Guest
    • Total Pages
      256
    • Publisher
      Amer. Math. Soc.
    • Related Report
      2006 Annual Research Report
  • [Book] Arrangements, local systems and singularities(分担執筆)

    • Author(s)
      F. Elzein, et.al. (ed.)
    • Publisher
      Birkhauser(印刷中)
    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.sci.hokudai.ac.jp/~terao/

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://www.math.sci.hokudai.ac.jp/~terao/

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2005-04-01   Modified: 2021-04-07  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi