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 \'etale double cover of a Lagrangian subscheme in the corresponding moduli scheme on the associated covering K3 surface.
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