Arithmetic moduli and lifting of Enriques surfaces
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Christian Liedtke
Abstract
We construct the moduli space of Enriques surfaces in positive characteristic and eventually over the integers, and determine its local and global structure. As an application, we show lifting of Enriques surfaces to characteristic zero. The key observation is that the canonical double cover of an Enriques surface is birational to the complete intersection of three quadrics in ℙ5, even in characteristic 2.
Funding source: DFG
Award Identifier / Grant number: LI 1906/1-1
Funding source: DFG
Award Identifier / Grant number: Transregio SFB 45
It is pleasure for me to thank Brian Conrad, Igor Dolgachev, David Eisenbud, Jack Hall, Sven Meinhardt, and especially Torsten Ekedahl for discussions and help. Also, I thank the referee for remarks and comments.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Cosmetic surgeries on knots in S3
- Integral points in two-parameter orbits
- Arithmetic moduli and lifting of Enriques surfaces
- Analytic varieties with finite volume amoebas are algebraic
- Vanishing resonance and representations of Lie algebras
- A new notion of angle between three points in a metric space
- Asymptotics of the Yang–Mills flow for holomorphic vector bundles over Kähler manifolds: The canonical structure of the limit
- An Oka principle for equivariant isomorphisms
- Birkhoff matrices, residues and rigidity for q-difference equations
Articles in the same Issue
- Frontmatter
- Cosmetic surgeries on knots in S3
- Integral points in two-parameter orbits
- Arithmetic moduli and lifting of Enriques surfaces
- Analytic varieties with finite volume amoebas are algebraic
- Vanishing resonance and representations of Lie algebras
- A new notion of angle between three points in a metric space
- Asymptotics of the Yang–Mills flow for holomorphic vector bundles over Kähler manifolds: The canonical structure of the limit
- An Oka principle for equivariant isomorphisms
- Birkhoff matrices, residues and rigidity for q-difference equations
