Descent of tautological sheaves from Hilbert schemes to Enriques manifolds

Let X be a K3 surface which doubly covers an Enriques surface S . If n∈ 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.