Revista Matemática Iberoamericana


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Published online first: 2019-11-11
DOI: 10.4171/rmi/1152

Zariski K3 surfaces

Toshiyuki Katsura[1] and Matthias Schütt[2]

(1) The University of Tokyo, Japan
(2) Leibniz-Universität Hannover, Germany and Riemann Center for Geometry and Physics, Hannover, Germany

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 $p\not\equiv 1$ mod 12. Our methods combine different approaches such as quotients by the group scheme $\alpha_p$, Kummer surfaces, and automorphisms of hyperelliptic curves.

Keywords: K3 surface, Zariski surface, abelian surface, infinitesimal group scheme, automorphism

Katsura Toshiyuki, Schütt Matthias: Zariski K3 surfaces. Rev. Mat. Iberoam. Electronically published on November 11, 2019. doi: 10.4171/rmi/1152 (to appear in print)