Birational geometry of moduli spaces of stable objects on Enriques surfaces

TL;DR

This paper studies the birational geometry of moduli spaces of stable objects on Enriques surfaces, establishing their equivalence under wall-crossing and relating them to Hilbert schemes, with new Chow-theoretic insights.

Contribution

It proves birational equivalences of moduli spaces on Enriques surfaces using wall-crossing and introduces a novel Chow-theoretic result linking these spaces to constant cycle subvarieties.

Findings

Moduli spaces are birationally equivalent under different stability conditions.

For odd rank Mukai vectors, they are birational to Hilbert schemes.

New Chow-theoretic result on constant cycle subvarieties.

Abstract

Using wall-crossing for K3 surfaces, we establish birational equivalence of moduli spaces of stable objects on generic Enriques surfaces for different stability conditions. As an application, we prove in the case of a Mukai vector of odd rank that they are birational to Hilbert schemes. The argument makes use of a new Chow-theoretic result, showing that moduli spaces on an Enriques surface give rise to constant cycle subvarieties of the moduli spaces of the covering K3.