Birational-geometric property of moduli of stable sheaves on surfaces

2015 Fiscal Year Final Research Report

• 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
• 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

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.

Free Research Field

複素代数幾何学