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arXiv · 1902.01579

K3 surfaces with 9 cusps in characteristic p

Toshiyuki Katsura·Matthias Schütt
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Abstract

We study K3 surfaces with 9 cusps, i.e. 9 disjoint $A_2$ configurations of smooth rational curves, over algebraically closed fields of characteristic $p\neq 3$. Much like in the complex situation studied by Barth, we prove that each such surface admits a triple covering by an abelian surface. Conversely, we determine which abelian surfaces with order three automorphisms give rise to K3 surfaces. We also investigate how K3 surfaces with 9 cusps hit the supersingular locus.

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Toshiyuki Katsura, Matthias Schütt. 2019-02-05. K3 surfaces with 9 cusps in characteristic p. https://arxiv.org/abs/1902.01579

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