Descent of tautological sheaves from Hilbert schemes to Enriques manifolds

Abstract

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