Study of moduli of algebraic vector bundles

2014 Fiscal Year Final Research Report

• Project/Area Number: 23740026
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Kumamoto University
• Principal Investigator: ABE Takeshi 熊本大学, 自然科学研究科, 准教授 (90362409)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: ベクトル束 / モジュライ

Outline of Final Research Achievements

There is a mysterious phenomenon called ``strange duality’’ in the study of moduli spaces of semistable sheaves on projective varieties. This is a phenomenon where the vector spaces of global sections of certain line bundles on certain two moduli spaces. In the case of curves, most strange dualities have been settled, but in the case of surfaces, there remain unsolved problems. In this study, we gave proofs to some cases of strange dualities for the projective plane and K3 surfaces. We also proved a factorization theorem for the spaces of generalized theta functions on the moduli of special orthogonal bundles.

Free Research Field

代数幾何学