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Moduli of coherent sheaves and complexes

Research Project

Project/Area Number 18H01113
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 11010:Algebra-related
Research InstitutionKobe University

Principal Investigator

Yoshioka Kota  神戸大学, 理学研究科, 教授 (40274047)

Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥14,170,000 (Direct Cost: ¥10,900,000、Indirect Cost: ¥3,270,000)
Fiscal Year 2022: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2021: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2020: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2019: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2018: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
KeywordsK3曲面、Enriques曲面 / アーベル曲面 / Brill-Noether / 安定層 / K3曲面 / 安定性 / ベクトル束 / 複体 / 正則symplectic多様体 / モジュライ / 連接層 / 代数多様体 / coherent sheaf / complex
Outline of Final Research Achievements

I studied the birational geometry of stable sheaves on Enriques surfaces. In particular, with Howard Nuer, I proved that the moduli of odd rank stable sheaves is birationally equivalent to the Hilbert scheme of points. For the moduli of stable sheaves on a K3 surface with the Picard rank 1, I studied weak Brill-Noether property. This is a joint work with Izzet Coskun and Howard Nuer. For the derived category of an abelian surface, I calculated the categorical entropy of some endofunctor. In particular I confirmed a conjecture of Kikuta and Takahashi in this case.I also studied the birational automorphism group of a generalized Kummer variety.

Academic Significance and Societal Importance of the Research Achievements

安定層やそのモジュライは微分幾何やYang-Mills理論(インスタントン)と関係し、様々な立場から研究がなされてきた。特に標準束が自明あるいはそれに近い場合、モジュライ空間の標準束も自明あるいはそれに近くなり代数幾何学的に興味深い構造を持っている。この研究ではEnriques曲面や楕円曲面上のモジュライについての双有理同型類、genericな安定層のコホモロジー群の挙動、圏論的エントロピーなどについて成果を得ることができた。

Report

(6 results)
  • 2023 Final Research Report ( PDF )
  • 2022 Annual Research Report
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • Research Products

    (17 results)

All 2024 2023 2022 2021 2020 2019 Other

All Int'l Joint Research (3 results) Journal Article (8 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 8 results) Presentation (6 results) (of which Int'l Joint Research: 6 results,  Invited: 6 results)

  • [Int'l Joint Research] University of Illinois Chicago(米国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] Israel Institute of Technology(イスラエル)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] イリノイ大学シカゴ校(米国)

    • Related Report
      2020 Annual Research Report
  • [Journal Article] Birational automorphim groups of a generalized Kummer manifold for an abelian surface with Picard number 12024

    • Author(s)
      Yoshioka Kota
    • Journal Title

      manuscripta mathematica

      Volume: 173 Issue: 1-2 Pages: 727-751

    • DOI

      10.1007/s00229-023-01472-9

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wall crossing for moduli of stable sheaves on an elliptic surface2024

    • Author(s)
      Yoshioka Kota
    • Journal Title

      Mathematische Zeitschrift

      Volume: 306 Issue: 1

    • DOI

      10.1007/s00209-023-03410-7

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The cohomology of the general stable sheaf on a K3 surface2023

    • Author(s)
      Coskun Izzet、Nuer Howard、Yoshioka Kota
    • Journal Title

      Advances in Mathematics

      Volume: 426 Pages: 109102-109102

    • DOI

      10.1016/j.aim.2023.109102

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Some moduli spaces of 1-dimensional sheaves on an elliptic ruled surface2023

    • Author(s)
      Yoshioka Kota
    • Journal Title

      Geometriae Dedicata

      Volume: 217 Issue: 3

    • DOI

      10.1007/s10711-023-00801-2

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Moduli of Stable Sheaves on a K3 Surface of Picard Number 12022

    • Author(s)
      MORI Akira、YOSHIOKA Kota
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 45 Issue: 2 Pages: 263-298

    • DOI

      10.3836/tjm/1502179369

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] aCM bundles on a general abelian surface2021

    • Author(s)
      Yoshioka Kota
    • Journal Title

      Archiv der Mathematik

      Volume: 116

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] MMP via wall-crossing for moduli spaces of stable sheaves on an Enriques surface2020

    • Author(s)
      Nuer, Howard, Yoshioka, Kota
    • Journal Title

      Adv. Math.

      Volume: 372

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Categorical entropy for Fourier-Mukai transforms on generic abelian surfaces2020

    • Author(s)
      Kota Yoshioka
    • Journal Title

      J. Algebra

      Volume: 556 Pages: 448-446

    • DOI

      10.1016/j.jalgebra.2020.03.019

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Presentation] Moduli of stable sheaves on an elliptic surface2023

    • Author(s)
      Yoshioka Kota
    • Organizer
      Gauge Theory, Moduli Spaces and Representation Theory, Kyoto 2023. In honor of the 60th birthday of Hiraku Nakajima
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Moduli of stable sheaves on an elliptic surface2022

    • Author(s)
      Yoshioka Kota
    • Organizer
      Workshop in honour of Lothar Goettsche's 60th birthday, 13-16 December 2021,
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Moduli of stable sheaves on an abelian surface2022

    • Author(s)
      Yoshioka Kota
    • Organizer
      Japanese-European Symposium on symplectic varieties and moduli spaces, 14--18, March 2022, 早稲田大学理工学部
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Weak Brill-Noether for the moduli of stable sheaves on a generic K3 surface2019

    • Author(s)
      Kota Yoshioka
    • Organizer
      fourth Japanese-European Symposium on Symplectic Varieties and Moduli Spaces
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Moduli of stable sheaves on Enriques surfaces2019

    • Author(s)
      Kota Yoshioka
    • Organizer
      School and Workshop on Gauge Theories and Differential Invariants
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Weak Brill-Noether for the moduli of stable sheaves on a generic K3 surface2019

    • Author(s)
      Kota Yoshioka
    • Organizer
      Categorical and Analytic Invariants in Algebraic Geometry VII
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited

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Published: 2018-04-23   Modified: 2025-01-30  

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