Strange Duality for elliptic surfaces

TL;DR

This paper proves the Strange Duality conjecture for elliptic surfaces by reducing the problem to Hilbert schemes using Bridgeland's isomorphisms, building on Marian-Oprea's theorem.

Contribution

It establishes the Strange Duality for elliptic surfaces, extending the understanding of dualities in moduli spaces of stable sheaves.

Findings

Proof of Strange Duality for elliptic surfaces

Reduction to Hilbert schemes via Bridgeland's isomorphisms

Utilization of Marian-Oprea's theorem

Abstract

The main result of the present paper is the proof of the Strange Duality for elliptic surfaces -- a duality between global sections of determinantal line bundles on moduli spaces of stable sheaves on a fixed elliptic surface. For this, we employ the "Marian-Oprea trick": using Bridgeland's birational isomorphisms, we reduce the problem from a pair of general moduli spaces to a pair of Hilbert schemes. The latter case is a theorem by Marian-Oprea.