Descent of tautological sheaves from Hilbert schemes to Enriques manifolds

Abstract

Let X be a K3 surface which doubly covers an Enriques surface S. If n∈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 Schröer. In this paper we construct slope stable sheaves on S[n] and study some of their properties.