Birational-geometric property of moduli of stable sheaves on surfaces

• Project/Area Number: 23740037
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Okayama University of Science
• Principal Investigator: Yamada Kimiko 岡山理科大学, 理学部, 准教授 (70384170)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: モジュライ / ベクトル束 / 小平次元 / 特異点 / 楕円曲面 / エンリケス曲面 / 双有理幾何学 / 安定層 / 飯高プログラム / 安定連接層 / 代数曲面 / 変形理論 / 双有理幾何 / モジュライ空間 / 安定層のモジュライ / 倉西理論 / 高次元多様体の双有理幾何 / 標準特異点

Outline of Final Research Achievements

Let X be a complex projective surface, and H be an ample line bundle on X. There is a moduli scheme M(H) of H-stable vector bundles on X with fixed Chern classes. M(H) is a specific example of higher-dimensional algebraic variety. In birational geometry, there are several methods and theories to study higher-dimensional varieties V. In this research, we aimed at constructing and interpreting them by moduli-theoretic way in case where V is M(H). Consequently, we calculated the Kodaira dimension of M(H) when (1) X is an Enriques surface or (2) X is an elliptic surface with Kodaira dimension 1 and X has a few singular fibers.

Research Products

• [Presentation] Singularities on moduli scheme of stable sheaves of Elliptic surfaces (2014)
  • Author(s): Kimiko Yamada
  • Organizer: 第59回代数学シンポジウム
  • Place of Presentation: 東京大学
  • Year and Date: 2014-09-09
  • Invited
• [Presentation] Singularities and Kodaira dimension of moduli scheme of sheaves on Enriques surfaces (2012)
  • Author(s): Kimiko Yamada.
  • Organizer: 研究集会「高次元双有理幾何の周辺」
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] Singularities and Kodaira dimension of moduli scheme of sheaves on Enriques surfaces (ポスター発表） (2012)
  • Author(s): Kimiko Yamada.
  • Organizer: Conference ``Algebraic and complex geometry''
  • Place of Presentation: Leibniz Universtat Hannover, ドイツ
• [Presentation] Sigularities and Kodaira dimension of moduli of stable sheaves on Enriques surfaces
  • Author(s): 山田紀美子
  • Organizer: 東京大学 代数幾何セミナー
  • Place of Presentation: 東京大学