A tour of theta dualities on moduli spaces of sheaves

TL;DR

This paper surveys known theta dualities on moduli spaces of sheaves and introduces new dualities, especially on elliptic K3 surfaces, proposing conjectures that relate to strange duality.

Contribution

It provides a comprehensive survey and establishes new theta dualities on surfaces, notably on elliptic K3 surfaces, with conjectures linking to strange duality.

Findings

New theta dualities on surface moduli spaces are established.

Detailed study of elliptic K3 surfaces enhances understanding of dualities.

Proposed conjectures connect dualities to the phenomenon of strange duality.

Abstract

The purpose of this paper is twofold. First, we survey known results about theta dualities on moduli spaces of sheaves on curves and surfaces. Secondly, we establish new such dualities in the surface case. Among others, the case of elliptic K3 surfaces is studied in detail; we propose further conjectures which are shown to imply strange duality.