On exceptional Enriques surfaces

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.

19 pages. This version gives a different presentation of the combinatorics involved

References in corpus (1)

• Equations for some very special Enriques surfaces in characteristic two

Cited by in corpus (4)

• Moduli and periods of simply connected Enriques surfaces
• Equations for some very special Enriques surfaces in characteristic two
• Weyl group covers for Brieskorn's resolutions in all characteristics and the integral cohomology of $G/P$
• On Enriques surfaces in characteristic 2 with a finite group of automorphisms