Birational geometry of moduli spaces of algebraic sheaves

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04824
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kumamoto University
• Principal Investigator: ABE Takeshi 熊本大学, 大学院先端科学研究部(理), 准教授 (90362409)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 代数的層 / モジュライ空間

Outline of Final Research Achievements

There is a theta divisor on the Picard group, the set of linear equivalence classes of divisors, of a compact Riemann surface. As a ``non-abelian analogue’’, we have a generalized theta divisor on the moduli space of algebraic vector bundles on a compact Riemann surface. A global section of the line bundle associated with a generalized theta divisor is called a generalized theta function. We have an interesting phenomena called Strange duality about generalized theta functions. It is conjectured that we also have Strange duality phenomena for moduli spaces of sheaves on projective surfaces. I once proved partially the strange duality conjecture for projective plane. In this research, continuing the preceding research, I proved some cases of the strange duality conjecture for a quadric surface.

Free Research Field

代数幾何学