JournalsrmiVol. 36, No. 3pp. 869–894

Zariski K3 surfaces

  • Toshiyuki Katsura

    The University of Tokyo, Japan
  • Matthias Schütt

    Leibniz-Universität Hannover, Germany and Riemann Center for Geometry and Physics, Hannover, Germany
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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 p≢1p\not\equiv 1 mod 12. Our methods combine different approaches such as quotients by the group scheme αp\alpha_p, Kummer surfaces, and automorphisms of hyperelliptic curves.

Cite this article

Toshiyuki Katsura, Matthias Schütt, Zariski K3 surfaces. Rev. Mat. Iberoam. 36 (2020), no. 3, pp. 869–894

DOI 10.4171/RMI/1152