Descent of tautological sheaves from Hilbert schemes to Enriques manifolds

TL;DR

This paper constructs and studies slope stable sheaves on Enriques manifolds obtained as quotients of Hilbert schemes of points on K3 surfaces, revealing new geometric structures.

Contribution

It introduces a method to construct slope stable sheaves on Enriques manifolds derived from Hilbert schemes of K3 surfaces.

Findings

Construction of slope stable sheaves on Enriques manifolds

Analysis of properties of these sheaves

Extension of stability concepts to new geometric contexts

Abstract

Let $X$ be a K3 surface which doubly covers an Enriques surface $S$. If $n\in\mathbb{N}$ is an odd number, then the Hilbert scheme of $n$-points $X^{[n]}$ admits a natural quotient $S_{[n]}$. This quotient is an Enriques manifold in the sense of Oguiso and Schr\"oer. In this paper we construct slope stable sheaves on $S_{[n]}$ and study some of their properties.