On moduli spaces of semistable sheaves on Enriques surfaces

TL;DR

This paper investigates the structure of one-dimensional moduli spaces of rank 2 Gieseker semistable sheaves on Enriques surfaces, providing new descriptions and reduction techniques for high-rank cases.

Contribution

It improves previous results on moduli spaces of sheaves on Enriques surfaces and introduces methods to reduce high-rank problems to low ranks, especially for unnodal surfaces.

Findings

Moduli spaces are reducible for nodal Enriques surfaces under general polarizations.

Reduction techniques connect high even ranks to low ranks for unnodal surfaces.

Enhanced understanding of the geometry of sheaves on Enriques surfaces.

Abstract

We describe some one-dimensional moduli spaces of rank 2 Gieseker semistable sheaves on an Enriques surface improving earlier results of H. Kim. In case of a nodal Enriques surface the obtained moduli spaces are reducible for general polarizations. For unnodal Enriques surfaces we show how to reduce the study of moduli spaces of high even rank Gieseker semistable sheaves to low ranks. To prove this we use the method of K. Yoshioka who showed that in the odd rank one can reduce to rank 1.