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Geometry and combinatorics of hyperplane arrangements

Research Project

Project/Area Number 20740038
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionKobe University

Principal Investigator

YOSHINAGA Masahiko  Kobe University, 理学研究科, 助教 (90467647)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords超平面配置 / 対数的ベクトル場 / 極小セル分割
Research Abstract

In the first year, I studied the sheaf of logarithmic vector fields associated to divisors on the projective space. I obtained several results on Torelli-type theorem for generic hypersurface (Collaboration with K. Ueda) and on the freeness for hyperplane arrangements with multiplicities. In the second and third year, I studied minimality of hyperplane arrangements and applications. I obtained new presentations for fundamental groups and a characterization for vanishing twisted cohomology groups.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (34 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (16 results) (of which Peer Reviewed: 15 results) Presentation (18 results)

  • [Journal Article] Coxeter multiarrangements with quasi-constant multiplicities.2009

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

      Journal of Algebra. 322

      Pages: 2839-2847

    • NAID

      120006459575

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Chamber basis of the Orlik-Solomon algebra and Aomoto complex.2009

    • Author(s)
      Masahiko Yoshinaga
    • Journal Title

      Arkiv for Matematik 47

      Pages: 393-407

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Logarithmic vector fields along smooth divisors in projective spaces.2009

    • Author(s)
      Kazushi Ueda, Masahiko Yoshinaga
    • Journal Title

      Hokkaido Mathematical Jorunal Vol.38, No.3

      Pages: 409-415

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Totally free arrangements of hyperplanes.2009

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

      Proc.A.M.S. 137

      Pages: 1405-1410

    • NAID

      120006459611

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Logarithmic vector fields along smooth divisors in projective spaces.2009

    • Author(s)
      K.Ueda, M.Yoshinaga
    • Journal Title

      Hokkaido Mathematical Jorunal 38

      Pages: 409-415

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Chamber basis of the Orlik-Solomon algebra and Aomoto complex.2009

    • Author(s)
      M.Yoshinaga
    • Journal Title

      Arkiv for Matematik 47

      Pages: 393-407

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Coxeter multiarrangements with quasi-constant multiplicities.2009

    • Author(s)
      T.Abe, M.Yoshinaga
    • Journal Title

      Journal of Algebra 322

      Pages: 2839-2847

    • NAID

      120006459575

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Jacobian ideal of a hyperplane arrangement.2008

    • Author(s)
      Max Wakefield, Masahiko Yoshinaga
    • Journal Title

      Mathematical Research Letteres Vol.15, no.4

      Pages: 795-799

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Logarithmic vector fields along smooth plane cubic curves.2008

    • Author(s)
      Kazushi Ueda, Masahiko Yoshinaga
    • Journal Title

      Kumamoto Journal of Mathematics Vol.21

      Pages: 11-20

    • NAID

      110009930082

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generic section of a hyperplane arrangement and twisted Hurewicz maps.2008

    • Author(s)
      Masahiko Yoshinaga
    • Journal Title

      Topology and its applications 55

      Pages: 1022-1026

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Splitting criterion for reflexive sheaves.2008

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

      Proc.A.M.S. 136

      Pages: 1887-1891

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Logarithmic vector fields along smooth plane cubic curves2008

    • Author(s)
      K. Ueda, and M. Yoshinaga
    • Journal Title

      Kumamoto Journal of Mathematics 21

      Pages: 11-20

    • NAID

      110009930082

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Jacobian ideal of a hyperplane arrangement2008

    • Author(s)
      M. Wakefield and M. Yoshinaga
    • Journal Title

      Mathematical Research Letters 15

      Pages: 795-799

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the extendability of free multiarrangements.2007

    • Author(s)
      Masahiko Yoshinaga
    • Journal Title

      Arrangements, Local Systems and Singularities : CIMPA Summer School,Galatasaray University, Istanbul

      Pages: 273-281

    • Related Report
      2010 Final Research Report
  • [Journal Article] Arrangements, multiderivations, and adjoint quotient map of type ADE.

    • Author(s)
      Masahiko Yoshinaga
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: (掲載決定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Minimality of hyperplane arrangements and basis of local system cohomology.

    • Author(s)
      Masahiko Yoshinaga
    • Journal Title

      IRMA Lectures in Mathematics and Theoretical Physics

      Volume: (掲載決定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] On the irreducibility of moduli spaces of line arrangements2011

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      Branched Coverings, Degenerations, and Related Topics 2011
    • Place of Presentation
      Tokyo Metroplitan University
    • Year and Date
      2011-03-08
    • Related Report
      2010 Final Research Report
  • [Presentation] Minimal Stratifications for Line Arrangements2011

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      The 6th Kagoshima Algebra-Analysis-Geometry Seminar
    • Place of Presentation
      Kagoshima University
    • Year and Date
      2011-02-15
    • Related Report
      2010 Final Research Report
  • [Presentation] On the irreducibility of moduli spaces of line arrangements2011

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      Topology of Singularities and the related geometry
    • Place of Presentation
      Tohoku University
    • Year and Date
      2011-01-05
    • Related Report
      2010 Final Research Report
  • [Presentation] Minimal Stratifications for Line Arrangements2011

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      Workshop on Geometry and Analysis of Discriminants
    • Place of Presentation
      IPMU
    • Related Report
      2010 Final Research Report
  • [Presentation] On the free arrangements and truncated affine Weyl arrangements.2010

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      KAIST Discrete Math Seminar, KAIST
    • Place of Presentation
      Daejeon, Korea
    • Year and Date
      2010-10-26
    • Related Report
      2010 Final Research Report
  • [Presentation] Modules of logarithmic derivations and applications to enumerative problems of hyperplane arrangements.2010

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      2010 Global KMS International Conference, POSTECH
    • Place of Presentation
      Pohang, Korea
    • Year and Date
      2010-10-22
    • Related Report
      2010 Final Research Report
  • [Presentation] Minimal Stratification for Line Arrangements.2010

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      Combinatorial and Geometric aspects of Hyperplane Arrangements
    • Place of Presentation
      Centro di Ricerca Matematica ``Ennio De Giorgi'' Pisa
    • Year and Date
      2010-05-25
    • Related Report
      2010 Final Research Report
  • [Presentation] Minimal presentations for the fundamental groups of the complement of hyperplane arrangements.2010

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      Interplay between representation theory and geometry
    • Place of Presentation
      Tsinghua University, China
    • Year and Date
      2010-05-03
    • Related Report
      2010 Final Research Report
  • [Presentation] Minimal presentations for the fundamental groups of the complement of hyperplane arrangements.2010

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      Interplay between representation theory and geometry
    • Place of Presentation
      Tsinghua University, Beijing, China(招待講演)
    • Year and Date
      2010-05-03
    • Related Report
      2010 Annual Research Report
  • [Presentation] Minimal presentations for the fundamental groups of the complement of hyperplane arrangements.2010

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      SEMINARI DI GEOMETRIA
    • Place of Presentation
      Universita di Pisa, Italy
    • Year and Date
      2010-04-15
    • Related Report
      2010 Final Research Report
  • [Presentation] Minimal presentations for the fundamental groups of the complement of hyperplane arrangements.2010

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      Topology of Singularities and the related geometry
    • Place of Presentation
      Hanoi, Vietnam
    • Year and Date
      2010-03-23
    • Related Report
      2010 Final Research Report
  • [Presentation] 超平面配置のトポロジー:極小性とその周辺2010

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      北海道大学数学教室談話会
    • Place of Presentation
      北海道大学
    • Year and Date
      2010-02-18
    • Related Report
      2010 Final Research Report
  • [Presentation] Orlik-Solomon代数と青本複体のChamber基底2010

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      超幾何方程式研究会2010
    • Place of Presentation
      神戸大学
    • Year and Date
      2010-01-07
    • Related Report
      2010 Final Research Report
  • [Presentation] Hyperplane arrangements and Lefschetz hyperplane section theorem.2009

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      5-th Franco-Japanese Symposium on Singularities
    • Place of Presentation
      Strasbourg
    • Year and Date
      2009-08-25
    • Related Report
      2010 Final Research Report
  • [Presentation] Hyperplane arrangements and Lefschetz hyperplane section theorem.2009

    • Author(s)
      M.Yoshinaga
    • Organizer
      5-th Franco-Japanese Symposium on Singularities
    • Place of Presentation
      Strasbourg, France
    • Year and Date
      2009-08-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] ねじれホモロジーの消滅定理とねじれHurewicz写像2009

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      超平面配置のさまざまな側面
    • Place of Presentation
      神戸大学
    • Year and Date
      2009-02-13
    • Related Report
      2010 Final Research Report
  • [Presentation] Arrangements and Algebraic Geometry (Survey lecture, 3hrs)2009

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      日本数学会季期研究集会Arrangements of Hyperplanes
    • Place of Presentation
      北海道大学
    • Related Report
      2010 Final Research Report
  • [Presentation] Minimality of hyperplane arrangements and applications2008

    • Author(s)
      Masahiko Yoshinaga
    • Organizer
      Geometry of Singularities and Manifolds
    • Place of Presentation
      草津
    • Year and Date
      2008-09-12
    • Related Report
      2010 Final Research Report 2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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