Rank one sheaves over quaternion algebras on Enriques surfaces
Algebraic Geometry
2019-10-30 v3
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.
Cite
@article{arxiv.1909.03867,
title = {Rank one sheaves over quaternion algebras on Enriques surfaces},
author = {Fabian Reede},
journal= {arXiv preprint arXiv:1909.03867},
year = {2019}
}
Comments
9 pages. Corrected typos, added proper reference for Theorem 3.2. Comments welcome