The Deligne–Illusie Theorem and exceptional Enriques surfaces

Abstract We give a notion of ordinary Enriques surfaces and their canonical lifts in any positive characteristic, and we prove Torelli-type results for this class of Enriques surfaces.

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On the periods of enriques surfaces, I

Proceedings of the Japan Academy ◽

10.3792/pja/1195517887 ◽

1977 ◽

Vol 53 (3) ◽

pp. 124-127 ◽

Cited By ~ 5

Author(s):

Eiji Horikawa

Keyword(s):

Enriques Surfaces

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Kummer's quartics and numerically reflective involutions of Enriques surfaces

Journal of the Mathematical Society of Japan ◽

10.2969/jmsj/06410231 ◽

2012 ◽

Vol 64 (1) ◽

pp. 231-246 ◽

Cited By ~ 3

Author(s):

Shigeru MUKAI

Keyword(s):

Enriques Surfaces

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Rank one sheaves over quaternion algebras on Enriques surfaces

Advances in Geometry ◽

10.1515/advgeom-2021-0027 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Fabian Reede

Keyword(s):

Quaternion Algebra ◽

Double Cover ◽

Complex Numbers ◽

K3 Surface ◽

Enriques Surface ◽

Quaternion Algebras ◽

Enriques Surfaces ◽

Rank One ◽

Torsion Free

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.

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