TY - JOUR

T1 - Q_l-cohomology projective planes and Enriques surfaces in characteristic two

AU - Schütt, Matthias

N1 - Funding information: Partial funding by ERC StG 279723 (SURFARI) is gratefully acknowledged.

PY - 2019/6/26

Y1 - 2019/6/26

N2 - 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).

AB - 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).

KW - Characteristic 2

KW - Elliptic fibration

KW - Enriques surface

KW - Fake projective plane

KW - Smooth rational curve

UR - http://www.scopus.com/inward/record.url?scp=85069595156&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1703.10441

DO - 10.48550/arXiv.1703.10441

M3 - Article

AN - SCOPUS:85069595156

VL - 3

JO - Epijournal de Geometrie Algebrique

JF - Epijournal de Geometrie Algebrique

M1 - 10

ER -