Moduli spaces of stable sheaves over quasi-polarized surfaces, and the relative Strange Duality morphism

TL;DR

This paper constructs relative moduli spaces of stable sheaves over quasipolarized surfaces using good moduli space theory and extends the relative Strange Duality morphism to quasipolarized K3 surfaces.

Contribution

It introduces a new construction of relative moduli spaces of stable sheaves over quasipolarized surfaces utilizing Alper's good moduli space theory.

Findings

Extended the relative Strange Duality morphism to quasipolarized K3 surfaces.

Constructed new relative moduli spaces of stable sheaves over quasipolarized surfaces.

Abstract

The main result of the present paper is a construction of relative moduli spaces of stable sheaves over the stack of quasipolarized projective surfaces. For this, we use the theory of good moduli spaces, whose study was initiated by Alper. As a corollary, we extend the relative Strange Duality morphism to the locus of quasipolarized K3 surfaces.