Singularities and Kodaira dimension of moduli scheme of stable sheaves on Enriques surfaces

TL;DR

This paper investigates the singularities and Kodaira dimension of moduli schemes of stable sheaves on Enriques and hyper-elliptic surfaces, showing they have canonical singularities and zero Kodaira dimension under certain conditions.

Contribution

It establishes that moduli schemes with expected dimension at least 7 have only canonical singularities and, if compact, possess Kodaira dimension zero.

Findings

Moduli schemes of stable sheaves have canonical singularities when dimension ≥ 7.

Compact moduli schemes have Kodaira dimension zero.

Results apply to Enriques and hyper-elliptic surfaces.

Abstract

Let M be a moduli scheme of stable sheaves with fixed Chern classes on an Enriques surface or a hyper-elliptic surface. If its expected dimension is 7 or more, then M admits only canonical singularities. Moreover, if M is compact, then its Kodaira dimension is zero.