Generic strange duality for $K3$ surfaces

TL;DR

This paper proves the generic strange duality conjecture for many cases on K3 surfaces, using Fourier-Mukai techniques and exploring implications for Brill-Noether theory, with an appendix on moduli space behavior.

Contribution

It establishes the isomorphism of strange duality for generic K3 surfaces in numerous cases, advancing understanding of moduli spaces and dualities in algebraic geometry.

Findings

Strange duality holds for generic K3 surfaces in many cases.

Fourier-Mukai techniques are effective in proving duality.

Applications to Brill-Noether theory for sheaves on K3 surfaces.

Abstract

Strange duality is shown to hold over generic $K3$ surfaces in a large number of cases. The isomorphism for elliptic $K3$ surfaces is established first via Fourier-Mukai techniques. Applications to Brill-Noether theory for sheaves on $K3$s are also obtained. The appendix written by Kota Yoshioka discusses the behavior of the moduli spaces under change of polarization, as needed in the argument.