On the strange duality conjecture for abelian surfaces

2012/07/23 by Alina Marian, Marian, Alina, Dragos Oprea +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1207.5307

arxiv created 2012/07/23 · openalex publication_date 2012/07/23 · arxiv updated 2012/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of equal ranks and fiber degree 1. The birational type of the moduli space of sheaves is also investigated. Generalizations to arbitrary product elliptic surfaces are given.

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