Strange duality on elliptic and K3 surfaces

Abstract

The Strange Duality is a conjectural duality between two spaces of global sections of natural line bundles on moduli spaces of sheaves on a fixed variety. It has been proved in full generality on curves by Marian and Oprea, and by Belkale. There have been ongoing work on the Strange Duality on surfaces by various people. In the current paper, we show that the approach of Marian and Oprea to treating elliptic surfaces can be generalized in multiple directions: first, we can prove the Strange Duality in many cases over elliptic surfaces, and then, we extend their moduli construction to the non-ample quasipolarized locus of K3 surfaces.