Q_l-cohomology projective planes and Enriques surfaces in characteristic two

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Original languageEnglish
Article number10
Number of pages24
JournalEpijournal de Geometrie Algebrique
Volume3
Publication statusPublished - 26 Jun 2019

Abstract

We classify singular Enriques surfaces in characteristic two supporting a rank nine configuration of smooth rational curves. They come in one-dimensional families defined over the prime field, paralleling the situation in other characteristics, but featuring novel aspects. Contracting the given rational curves, one can derive algebraic surfaces with isolated ADE-singularities and trivial canonical bundle whose Q`-cohomology equals that of a projective plane. Similar existence results are developed for classical Enriques surfaces. We also work out an application to integral models of Enriques surfaces (and K3 surfaces).

Keywords

    Characteristic 2, Elliptic fibration, Enriques surface, Fake projective plane, Smooth rational curve

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Q_l-cohomology projective planes and Enriques surfaces in characteristic two. / Schütt, Matthias.
In: Epijournal de Geometrie Algebrique, Vol. 3, 10, 26.06.2019.

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Schütt M. Q_l-cohomology projective planes and Enriques surfaces in characteristic two. Epijournal de Geometrie Algebrique. 2019 Jun 26;3:10. doi: 10.48550/arXiv.1703.10441, 10.46298/epiga.2019.volume3.3990
Schütt, Matthias. / Q_l-cohomology projective planes and Enriques surfaces in characteristic two. In: Epijournal de Geometrie Algebrique. 2019 ; Vol. 3.
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