Finite groups in the theory of K3 surfaces

• Project/Area Number: 15K17521
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Tokyo University of Science
• Principal Investigator: Ohashi Hisanori 東京理科大学, 理工学部数学科, 准教授 (40547006)
• Project Period (FY): 2015-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: エンリケス曲面 / K3曲面 / 自己同型 / エントロピー / サレム数 / 偏極 / モジュライ / 代数幾何学

Outline of Final Research Achievements

I have made studies and presentations in conferences/papers on the following topics, mainly on the geometry of automorphisms of Enriques surfaces, which are closely related to K3 surfaces. 1. New projective models and descriptions of moduli spaces of the type II Enriques surfaces. 2. On the dynamical degrees of automorphisms of Enriques surfaces. 3. Symmetries of order 4 on Enriques surfaces.

Academic Significance and Societal Importance of the Research Achievements

K3曲面やエンリケス曲面の自己同型は、1970年代に始まり現代にいたるまで、たくさんの研究者の興味を惹きつけてきた。その理由は、これらの曲面に対するトレリ型定理をはじめとする非常に抽象的な理論が、射影モデルや自己同型の記述といった非常に具体的な結論を導くという、大きな枠組みの魅力にあると感じられる。今回の一連の研究においても、この視点を押し進めて、エンリケス曲面上の自己同型を抽象的な格子理論で統制する様々な現象を記述することができた。

Research Products

• [Int'l Joint Research] Leibniz university of Hannover(ドイツ)
• [Int'l Joint Research] Ｊａｇｉｅｌｌｏｎｉａｎ ｕｎｉｖｅｒｓｉｔｙ(ポーランド)
• [Int'l Joint Research] Jagiellonian University(ポーランド)
• [Journal Article] サレム数とK3曲面の自己同型 (2018)
  • Author(s): 大橋久範
  • Journal Title: 数理科学 Volume: 664 Pages: 55-60
• [Journal Article] On automorphisms of Enriques surfaces and their entropy (2018)
  • Author(s): Y. Matsumoto, H. Ohashi, S. Rams
  • Journal Title: Mathematische Nachrichten Volume: 印刷中 Issue: 13 Pages: 2084-2098
  • DOI: 10.1002/mana.201700329
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Rationality of the moduli spaces of Eisenstein K3 surfaces (2015)
  • Author(s): Shouhei Ma, Hisanori Ohashi and Shingo Taki
  • Journal Title: Trans. Amer. Math. Soc. Volume: 367 Issue: 12 Pages: 8643-8679
  • DOI: 10.1090/tran/6349
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] Symmetries of order four on Enriques surfaces (2019)
  • Author(s): Hisanori Ohashi
  • Organizer: Research seimnar on algebraic and arithetic geometry
  • Int'l Joint Research
• [Presentation] Topological classification of automorphisms on Enriques surfaces of order 4 (2018)
  • Author(s): Hisanori Ohashi
  • Organizer: working workshop on Calabi-Yau varieties and related topics
  • Int'l Joint Research / Invited
• [Presentation] Topological classification of automorphisms on Enriques surfaces of order 4 (2018)
  • Author(s): Hisanori Ohashi
  • Organizer: Algebraic Geometry
  • Int'l Joint Research / Invited
• [Presentation] Automorphisms of Enriques surfaces of order 4 (2018)
  • Author(s): 大橋久範
  • Organizer: 代数幾何学研究集会 -宇部-
  • Invited
• [Presentation] On automorphisms of Enriques surfaces and their entropy (2018)
  • Author(s): Ohashi Hisanori
  • Organizer: 正標数の代数幾何とその関連する話題
  • Int'l Joint Research / Invited
• [Presentation] エンリケス曲面の自己同型の性質と、エントロピーについて (2017)
  • Author(s): 大橋久範
  • Organizer: 第15回代数曲面ワークショップat秋葉原
  • Invited
• [Presentation] On automorphisms of Enriques surfaces and their topological entropy (2017)
  • Author(s): Ohashi Hisanori
  • Organizer: Hakodate workshop on arithmetic geometry 2017
  • Int'l Joint Research / Invited
• [Presentation] On automorphisms of Enriques surfaces and their entropy (2017)
  • Author(s): Ohashi Hisanori
  • Organizer: Workshop on Calabi-Yau manifolds -arithmetic, geometry and physics-
  • Int'l Joint Research / Invited
• [Presentation] On automorphisms of Enriques surfaces and their entropy (2017)
  • Author(s): Hisanori Ohashi
  • Organizer: Japanese-European symposium on symplectic varieties and moduli spaces
  • Int'l Joint Research
• [Presentation] エンリケス曲面の自己同型とエントロピーについて (2017)
  • Author(s): 大橋久範
  • Organizer: 東京電機大学 数学講演会
  • Invited
• [Presentation] エンリケス曲面の自己同型とエントロピーについて (2017)
  • Author(s): 大橋久範
  • Organizer: 東工大 数論・幾何学セミナー
  • Invited
• [Presentation] On automorphisms of Enriques surfaces and their entropy (2017)
  • Author(s): 大橋久範
  • Organizer: 葉層構造の幾何学とその応用
  • Invited
• [Presentation] On automorphisms of Enriques surfaces and their entropy (2017)
  • Author(s): Ohashi Hisanori
  • Organizer: K3 surfaces and related topics
  • Int'l Joint Research / Invited
• [Presentation] エンリケス曲面の自己同型について (2016)
  • Author(s): Hisanori Ohashi
  • Organizer: 代数幾何セミナー
  • Place of Presentation: 名古屋大学（愛知県名古屋市）
  • Year and Date: 2016-03-03
  • Int'l Joint Research / Invited
• [Presentation] The automorphism groups of the Enriques surfaces covered by some symmetric quartic K3 surfaces (2016)
  • Author(s): Hisanori Ohashi
  • Organizer: Arithmetic and Algebraic Geometry 2016
  • Place of Presentation: 東京大学（東京都目黒区）
  • Year and Date: 2016-01-25
  • Int'l Joint Research / Invited
• [Presentation] エンリケス曲面の自己同型のエントロピーについて (2016)
  • Author(s): 大橋久範
  • Organizer: 代数幾何学セミナー
  • Place of Presentation: 名古屋大学（愛知県・名古屋市）
  • Invited
• [Presentation] エンリケス曲面の自己同型について (2016)
  • Author(s): 大橋久範
  • Organizer: 新潟代数セミナー
  • Place of Presentation: 新潟大学（新潟県・新潟市）
  • Invited
• [Presentation] Enriques surfaces of type II and an elliptic modular surface of level 4 (2016)
  • Author(s): 大橋久範
  • Organizer: 射影多様体の幾何とその周辺２０１６
  • Place of Presentation: 高知工科大学（高知県・高知市）
  • Invited
• [Presentation] Enriques surfaces of type II and an elliptic modular surface of level 4 (2016)
  • Author(s): Ohashi Hisanori
  • Organizer: On explicit description of holomorphic symplectic varieties
  • Place of Presentation: 大沼国際セミナーハウス（北海道・亀田郡七飯町）
  • Int'l Joint Research
• [Presentation] On Enriques surfaces of type II and some elliptic modular surfaces (2016)
  • Author(s): Ohashi Hisanori
  • Organizer: Calabi-Yau manifolds: arithmetic, geometry and physics
  • Place of Presentation: 津田塾大学（東京都・小平市）
  • Int'l Joint Research / Invited
• [Presentation] エンリケス曲面の自己同型について (2016)
  • Author(s): 大橋久範
  • Organizer: 談話会
  • Place of Presentation: 筑波大学（茨城県・つくば市）
  • Invited
• [Presentation] On some families of Enriques surfaces parametrized by rational modular curves (2016)
  • Author(s): Ohashi Hisanori
  • Organizer: Rationality and self-maps of algebraic varieties
  • Place of Presentation: 京都大学（京都府・京都市）
  • Int'l Joint Research / Invited
• [Presentation] On some families of Enriques surfaces parametrized by rational modular curves (2016)
  • Author(s): 大橋久範
  • Organizer: 代数幾何学セミナー
  • Place of Presentation: 九州大学（福岡県・福岡市）
  • Invited
• [Presentation] Curve configurations on Enriques surfaces and automorphism groups (2015)
  • Author(s): Hisanori Ohashi
  • Organizer: Singular curves on K3 surfaces and hyperkaehler manifolds
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach (Oberwolfach, Germany)
  • Year and Date: 2015-11-09
  • Int'l Joint Research / Invited
• [Presentation] エンリケス曲面の自己同型について (2015)
  • Author(s): 大橋久範
  • Organizer: 合同セミナー
  • Place of Presentation: 東京理科大学（東京都新宿区）
  • Year and Date: 2015-09-17
  • Invited
• [Presentation] Non-semi-symplectic automorphisms of Enriques surfaces (2015)
  • Author(s): Hisanori Ohashi
  • Organizer: Research seminar on algebraic and arithmetic geometry
  • Place of Presentation: Leibniz universitaet Hannover (Hannover, Germany)
  • Year and Date: 2015-09-07
  • Int'l Joint Research
• [Presentation] エンリケス曲面の自己同型について (2015)
  • Author(s): 大橋久範
  • Organizer: 代数学シンポジウム
  • Place of Presentation: 静岡大学（静岡県静岡市）
  • Year and Date: 2015-09-01
  • Invited
• [Presentation] Gorenstein Q-homology projective planes (2015)
  • Author(s): Hisanori Ohashi
  • Organizer: Joint Workshop: Geometry and Analysis
  • Place of Presentation: 東京理科大学（千葉県野田市）
  • Year and Date: 2015-05-15
  • Int'l Joint Research / Invited
• [Funded Workshop] Japanese-European symposium on symplectic varieties and moduli spaces --third edition-- (2018)
• [Funded Workshop] Japanese-European symposium on symplectic varieties and moduli spaces (2017)