On the strange duality conjecture for abelian surfaces

TL;DR

This paper investigates Le Potier's strange duality conjecture on abelian surfaces, proving the isomorphism for specific cases involving product of elliptic curves and analyzing the moduli space's birational properties.

Contribution

It establishes the isomorphism for certain abelian surfaces and extends the results to general product elliptic surfaces, advancing understanding of the conjecture.

Findings

Proves the isomorphism for product of elliptic curves with specific sheaf conditions

Analyzes the birational type of the moduli space of sheaves

Provides generalizations to arbitrary product elliptic surfaces

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.