Rank one sheaves over quaternion algebras on Enriques surfaces

Fabian Reede

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arXiv · 1909.03867

Rank one sheaves over quaternion algebras on Enriques surfaces

Fabian Reede

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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 \'{e}tale double cover of a Lagrangian subscheme in the corresponding moduli scheme on the associated covering K3 surface.

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Fabian Reede. 2019-09-09. Rank one sheaves over quaternion algebras on Enriques surfaces. https://arxiv.org/abs/1909.03867

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