Matthias Schütt - Q_l-cohomology projective planes and singular Enriques surfaces in characteristic two

epiga:3990 - Épijournal de Géométrie Algébrique, 26 juin 2019, Volume 3 - https://doi.org/10.46298/epiga.2019.volume3.3990
Q_l-cohomology projective planes and singular Enriques surfaces in characteristic twoArticle

Auteurs : Matthias Schütt

    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_l-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).

    Comment: 24 pages; v3: journal version, correcting 20 root types to 19 and ruling out the remaining type 4A_2+A_1 (in new section 11)


    Volume : Volume 3
    Publié le : 26 juin 2019
    Accepté le : 26 juin 2019
    Soumis le : 12 octobre 2017
    Mots-clés : Mathematics - Algebraic Geometry, Mathematics - Number Theory, 14J28, 14J27
    Financement :
      Source : OpenAIRE Graph
    • Arithmetic of algebraic surfaces; Financeur: European Commission; Code: 279723

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