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Automorphisms of algebraic surfaces and its applications

Research Project

Project/Area Number 23740010
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionTokyo University of Science (2012-2014)
Nagoya University (2011)

Principal Investigator

OHASHI Hisanori  東京理科大学, 理工学部, 講師 (40547006)

Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords代数曲面 / K3曲面 / エンリケス曲面 / 正則シンプレクティック多様体 / 自己同型 / 自己同型群 / モジュライ / 国際情報交換(韓国) / K3曲面 / 国際情報交換(ドイツ) / マシュー群 / 国際情報交換(ハノーバー大学)
Outline of Final Research Achievements

An algebraic variety is a geometric structure which is defined by polynomials in (complex) projective spaces. Among two-dimensional algebraic varieties, I studied K3 surfaces and Enriques surfaces which are generally considered to have good properties, from the viewpoint centered at their automorphism groups. One fundamental aspect of this study is the symmetry of the varieties and its equations. The other aspect would be that it relates good properties of algebraic surfaces to abstract groups, resulting in the realization of abstract groups.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (26 results)

All 2015 2014 2013 2012 2011

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (21 results) (of which Invited: 16 results)

  • [Journal Article] Gorenstein Q-homology projective planes2015

    • Author(s)
      D. Hwang, J. Keum and H. Ohashi
    • Journal Title

      Science China Mathematics

      Volume: 58 Issue: 3 Pages: 501-512

    • DOI

      10.1007/s11425-015-4978-4

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classification of involutions on Enriques surfaces2014

    • Author(s)
      H. Ito and H. Ohashi
    • Journal Title

      Michigan Mathematical Journal

      Volume: 63

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Enriques surfaces of Hutchinson-Gopel type and Mathieu automorphisms2013

    • Author(s)
      向井 茂,大橋久範
    • Journal Title

      "Arithmetic and Geometry of K3 surfaces and Calabi-Yau threefolds", Fields Institute Communications

      Volume: 67 Pages: 429-454

    • DOI

      10.1007/978-1-4614-6403-7_15

    • ISBN
      9781461464020, 9781461464037
    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] K3 surfaces and log del Pezzo surfaces of index three2012

    • Author(s)
      H. Ohashi and S. Taki
    • Journal Title

      manuscripta math.

      Volume: 139 Issue: 3-4 Pages: 443-471

    • DOI

      10.1007/s00229-011-0524-z

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Hutchinson-Weber involutions degenerate exactly when the Jacobian2012

    • Author(s)
      H.Ohashi
    • Journal Title

      Publ.RIMS

      Volume: 48(掲載確定) Issue: 1 Pages: 107-127

    • DOI

      10.2977/prims/63

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Finite groups of Enriques surfaces and the Mathieu group M122014

    • Author(s)
      H. Ohashi
    • Organizer
      String, lattice and moonshine
    • Place of Presentation
      立教大学池袋キャンパス(東京都)
    • Year and Date
      2014-12-04
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces2014

    • Author(s)
      H. Ohashi
    • Organizer
      K3, Enriques surfaces and related topics
    • Place of Presentation
      名古屋大学東山キャンパス(愛知県)
    • Year and Date
      2014-11-10
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] (Non-)semi-symplectic automorphisms of Enriques surfaces2014

    • Author(s)
      H. Ohashi
    • Organizer
      射影多様体の幾何とその周辺2014
    • Place of Presentation
      高知大学朝倉キャンパス(高知県)
    • Year and Date
      2014-11-02
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Non-semi-symplectic automorphisms of Enriques surfaces2014

    • Author(s)
      H. Ohashi
    • Organizer
      第八回玉原特殊多様体研究集会
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県)
    • Year and Date
      2014-09-18
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Non-semi-symplectic automorphisms of Enriques surfaces2014

    • Author(s)
      H. Ohashi
    • Organizer
      第二回K3 曲面・エンリケス曲面ワークショップ
    • Place of Presentation
      旭川市大雪クリスタルホール(北海道)
    • Year and Date
      2014-08-30
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] K3 曲面の自己同型とMathieu 群についてのサーベイ2014

    • Author(s)
      H. Ohashi
    • Organizer
      マシュームーンシャインに関する勉強会
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県)
    • Year and Date
      2014-08-26
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Non-semi-symplectic automorphisms of Enriques surfaces2014

    • Author(s)
      H. Ohashi
    • Organizer
      Mini-workshop on Calabi-Yau
    • Place of Presentation
      津田塾大学小平キャンパス(東京都)
    • Year and Date
      2014-08-07
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Non-semi-symplectic automorphisms of Enriques surfaces2014

    • Author(s)
      H. Ohashi
    • Organizer
      第七回代数曲面ワークショップat秋葉原
    • Place of Presentation
      首都大学東京秋葉原サテライトキャンパス(東京都)
    • Year and Date
      2014-07-19
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 4 次対称K3 曲面から決まるエンリケス曲面の自己同型群の決定2014

    • Author(s)
      大橋久範
    • Organizer
      日本数学会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Research-status Report
  • [Presentation] The automorphism groups of the Enriques surfaces covered by some symmetric quartic K32014

    • Author(s)
      Hisanori Ohashi
    • Organizer
      Moduli and self-maps
    • Place of Presentation
      京都大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On some lattice of interest related to the prime eleven2013

    • Author(s)
      大橋久範
    • Organizer
      玉原特殊多様体研究集会
    • Place of Presentation
      東大玉原国際セミナーハウス
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 複素K3 曲面の変形とモジュライと自己同型について2013

    • Author(s)
      大橋久範
    • Organizer
      K3 曲面・エンリケス曲面ワークショップ
    • Place of Presentation
      北海道教育大学 札幌駅前サテライト
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Integral points of some elliptic curve via the binary Golay code2013

    • Author(s)
      Hisanori Ohashi
    • Organizer
      Beyond the moonshine
    • Place of Presentation
      ホテル華の湯
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On automorphisms of Enriques surfaces2013

    • Author(s)
      H. Ohashi
    • Organizer
      Arithmetic and Algebraic Geometry 2013
    • Place of Presentation
      東京大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] The rationality of moduli spaces of Eisenstein K3 surfaces2013

    • Author(s)
      H. Ohashi
    • Organizer
      New trends s in Arithmetic and Geometry of Algebraic Surfaces
    • Place of Presentation
      CIRM(フランス)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Automorphisms of the octahedral Enriques surface2012

    • Author(s)
      大橋久範
    • Organizer
      高次元代数幾何の周辺
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] K3 曲面やエンリケス曲面の有限対称性の分類2012

    • Author(s)
      大橋久範
    • Organizer
      代数幾何講演会
    • Place of Presentation
      埼玉大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Log del Pezzo surfaces of index three with multiple smooth divisors2012

    • Author(s)
      大橋久範
    • Organizer
      第9回アフィン代数幾何学研究集会(招待講演)
    • Place of Presentation
      関西学院大学大阪梅田キャンパス
    • Related Report
      2011 Research-status Report
  • [Presentation] On automorphism groups of Enriques surfaces2011

    • Author(s)
      大橋久範
    • Organizer
      城崎代数幾何学シンポジウム(招待講演)
    • Place of Presentation
      兵庫県豊岡市
    • Related Report
      2011 Research-status Report
  • [Presentation] On automorphism groups of Enriques surfaces2011

    • Author(s)
      大橋久範
    • Organizer
      代数幾何ワークショップ2011(招待講演)
    • Place of Presentation
      法政大学
    • Related Report
      2011 Research-status Report
  • [Presentation] On automorphisms of Enriques surfaces2011

    • Author(s)
      大橋久範
    • Organizer
      Workshop on Arithmetic and Geometry of K3 surfaces and Calabi-Yau threefolds(招待講演)
    • Place of Presentation
      フィールズ研究所(カナダ)
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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