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Complexes on algebraic varieties and their moduli spaces

Research Project

Project/Area Number 26287007
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Algebra
Research InstitutionKobe University

Principal Investigator

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

Project Period (FY) 2014-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥11,440,000 (Direct Cost: ¥8,800,000、Indirect Cost: ¥2,640,000)
Fiscal Year 2017: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2016: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2015: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2014: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Keywordsモジュライ / 複体 / K3 / 安定層 / 安定性 / ベクトル束 / Bridgeland stability
Outline of Final Research Achievements

We obtained some results on moduli of semi-stable sheaves on K3 surfaces and abelian surfaces. In particular we described the local structure of the singular points and get an example of strange duality. We also proved Kawamata-Morrison's cone conjectures for two series of irreducible symplectic manifolds of Beauville.
For moduli spaces of stable sheaves on Enriques surfaces, we described the condition for the non-emptyness. We also obtained some results on the birational geometry of the moduli spaces by using Bridgeland stability conditions.

Academic Significance and Societal Importance of the Research Achievements

安定層とそのモジュライ空間は微分幾何やYang-Mills理論(インスタントン)と関係し、様々な立場から研究されてきた。本研究では多くのよい性質をもつ曲面であるK3曲面、アーベル曲面、Enriques曲面に対し、そのモジュライ空間の性質を調べた。とくにEnriques曲面上の安定層についてはこれまで研究があまり進んでいなかったが、この研究で安定層の存在性やモジュライの既約性など基本的な問題に成果を得ることができた。

Report

(6 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report

Research Products

(22 results)

All 2019 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (3 results) Journal Article (9 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 9 results,  Open Access: 1 results,  Acknowledgement Compliant: 7 results) Presentation (9 results) (of which Int'l Joint Research: 3 results,  Invited: 9 results) Funded Workshop (1 results)

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

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] グラスゴー大学(英国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] ボローニャ大学(イタリア)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Derived equivalent Hilbert schemes of points on K3 surfaces which are not birational2019

    • Author(s)
      Ciaran Meachan, Giovanni Mongardi, Kota Yoshioka
    • Journal Title

      Math, Z.

      Volume: 出版予定

    • DOI

      10.1007/s00209-019-02281-1

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] The wall-crossing behavior for Bridgeland's stability conditions on abelian and K3 surfaces2018

    • Author(s)
      H. Minamide, K. Yoshioka, S. Yanagida
    • Journal Title

      J. reine angew. Math.

      Volume: 0 Pages: 1-107

    • DOI

      10.1515/crelle-2015-0010

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Moduli spaces of stable sheaves on Enriques surfaces2017

    • Author(s)
      Kota Yoshioka
    • Journal Title

      Kyoto J. Math.

      Volume: -

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Fourier-Mukai duality for K3 surfaces via Bridgeland stability condition2017

    • Author(s)
      Kota Yoshioka
    • Journal Title

      J. Geometry and Physics

      Volume: -

    • DOI

      10.1016/j.geomphys.2016.08.011

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A note on stable sheaves on Enriques surfaces II2017

    • Author(s)
      Kota Yoshioka
    • Journal Title

      Manuscripta Math

      Volume: 153

    • DOI

      10.1007/s00229-016-0882-7

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the strange duality conjecture for abelian surfaces II2017

    • Author(s)
      B., Bolognese, A., Marian, D., Oprea, K., Yoshioka
    • Journal Title

      J. Algebraic Geometry

      Volume: 未定

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on stable sheaves on Enriques2016

    • Author(s)
      Yoshioka Kota
    • Journal Title

      Tohoku Math. J. (2)

      Volume: 未定

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Bridgeland's stability and the positive cone of the moduli spaces of stable objects on an abelian surface2016

    • Author(s)
      Kota Yoshioka
    • Journal Title

      Adv. Stud. Pure Math.

      Volume: 未定

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A proof of the Kawamata-Morrison Cone Conjecture for holomorphic symplectic varieties of K3 or generalized Kummer deformation type2015

    • Author(s)
      E., Markman, K., Yoshioka
    • Journal Title

      Int. Math. Res. Not. (IMRN)

      Volume: 24

    • DOI

      10.1093/imrn/rnv119

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Categorical entropy for Fourier-Mukai transforms on generic abelian surfaces2017

    • Author(s)
      Kota Yoshioka
    • Organizer
      Derived category and birational geometry
    • Place of Presentation
      大阪大学理学部
    • Year and Date
      2017-02-20
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Vector bundles on Enriques surfaces2017

    • Author(s)
      Kota Yoshioka
    • Organizer
      代数的層のモジュライの研究とその周辺
    • Place of Presentation
      数理解析研究所
    • Year and Date
      2017-02-01
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Moduli of stable sheaves on Enriques surfaces2017

    • Author(s)
      Yoshioka Kota
    • Organizer
      Japanese-Europian Symposium on Symplectic Varieties
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Moduli spaces of stable sheaves on Enriques surfaces2016

    • Author(s)
      Kota Yoshioka
    • Organizer
      Derived categories and Chow groups of hyperkaehler and Calabi-Yau varieties
    • Place of Presentation
      Simons center for geometry and physics, Stony Brook, NY, USA
    • Year and Date
      2016-09-19
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Moduli spaces of stable sheaves on Enriques surfaces2016

    • Author(s)
      Kota Yoshioka
    • Organizer
      On explicit description of holomorphic symplectic varieties,
    • Place of Presentation
      大沼国際セミナーハウス
    • Year and Date
      2016-08-29
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Fourier-Mukai duality for K3 surfaces2015

    • Author(s)
      K. Yoshioka
    • Organizer
      Vector bundles on algebraic curves 2015
    • Place of Presentation
      Warwick University, England
    • Year and Date
      2015-06-15
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Twisted stability and Bridgeland stability2015

    • Author(s)
      吉岡康太
    • Organizer
      Geometry from stability conditions
    • Place of Presentation
      Warwick University
    • Year and Date
      2015-02-16 – 2015-02-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Examples of movable divisors on a generalized Kummer variety and an application2014

    • Author(s)
      吉岡康太
    • Organizer
      代数幾何学シンポジウム
    • Place of Presentation
      城崎国際アートセンター
    • Year and Date
      2014-10-20 – 2014-10-24
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 代数曲面上のベクトル束2014

    • Author(s)
      吉岡康太
    • Organizer
      第59回代数学シンポジウム
    • Place of Presentation
      東大数理科学研究科
    • Year and Date
      2014-09-08 – 2014-09-11
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Funded Workshop] Algebraic Geometry and Integrable Systems, Kobe 20162016

    • Place of Presentation
      Faculty of Science, Kobe University
    • Year and Date
      2016-12-05
    • Related Report
      2016 Annual Research Report

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Published: 2014-04-04   Modified: 2022-02-22  

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