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arXiv · 1710.08661

Zariski K3 surfaces

Toshiyuki Katsura·Matthias Schütt
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Abstract

We construct Zariski K3 surfaces of Artin invariant 1, 2 and 3 in many characteristics. In particular, we prove that any supersingular Kummer surface is Zariski if the characteristic is not congruent to 1 modulo 12. Our methods combine different approaches such as quotients by the group scheme $\alpha_p$, Kummer surfaces, and automorphisms of elliptic and hyperelliptic curves.

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Toshiyuki Katsura, Matthias Schütt. 2017-10-24. Zariski K3 surfaces. https://arxiv.org/abs/1710.08661

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