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Singularities of normal quartic surfaces, III: char${}=2$, nonsupersingular

Fabrizio Catanese and Matthias Schütt

Vol. 5 (2023), No. 3, 457–478
Abstract

We show, in this third part, that the maximal number of singular points of a normal quartic surface X K3 defined over an algebraically closed field K of characteristic 2 is at most 12, if the minimal resolution of X is not a supersingular K3 surface. We also provide a family of explicit examples, valid in any characteristic.

Keywords
normal quartic surface, $\mathrm{K3}$ surface, elliptic fibration, rational double point
Mathematical Subject Classification
Primary: 14J17, 14J25, 14J28, 14N05, 14N25
Milestones
Received: 12 October 2022
Revised: 12 February 2023
Accepted: 26 February 2023
Published: 2 November 2023
Authors
Fabrizio Catanese
Mathematisches Institut
Universität Bayreuth
Germany
Korea Institute for Advanced Study
Seoul
South Korea
Matthias Schütt
Institut für Algebraische Geometrie
Leibniz Universität Hannover
Germany