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arXiv · 1703.10441

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

Matthias Schütt
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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_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).

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Matthias Schütt. 2017-03-30. Q_l-cohomology projective planes and singular Enriques surfaces in characteristic two. https://doi.org/10.46298/epiga.2019.volume3.3990

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