Rank one sheaves over quaternion algebras on Enriques surfaces

Abstract

Let X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra A on X. Then we study the moduli scheme of torsion free A-modules of rank one. Finally we prove that this moduli scheme is an étale double cover of a Lagrangian subscheme in the corresponding moduli scheme on the associated covering K3 surface.

9 pages. Corrected typos, added proper reference for Theorem 3.2. Comments welcome