Sheaves on abelian surfaces and Strange Duality

TL;DR

This paper proposes three versions of a strange duality conjecture for sheaves on abelian surfaces and provides evidence by verifying dimension equalities on dual moduli spaces.

Contribution

It introduces multiple formulations of the strange duality conjecture specifically for abelian surfaces and supports them through dimension calculations.

Findings

Dimension equalities verified on dual moduli spaces

Formulation of three versions of the strange duality conjecture

Addresses a question by Gottsche-Nakajima-Yoshioka

Abstract

We formulate three versions of a strange duality conjecture for sections of the Theta bundles on the moduli spaces of sheaves on abelian surfaces. As supporting evidence, we check the equality of dimensions on dual moduli spaces, answering a question raised by Gottsche-Nakajima-Yoshioka.