On exceptional Enriques surfaces

2004/05/26 by Torsten Ekedahl, Ekedahl, T., N. I. Shepherd‐Barron +1 · 2 citations
Mathematics · #14J27 (Secondary) #14J28 (Primary) #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.math/0405510

openalex publication_date 2004/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a complete description of all classical Enriques surfaces with non-zero global vector fields. In particular we show that there are such surfaces. The obtained result also applies to supersingular Enriques surfaces fulfilling a rather special condition. During this classification we study some properties of genus 1-fibrations special to characteristic as well as make a close study of the genus 1-fibration on the surfaces that we classify.

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• On Enriques surfaces in characteristic 2 with a finite group of automorphisms
• Equations for some very special Enriques surfaces in characteristic two
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