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

We show, in this third part, that the maximal number of singular points of a normal quartic surface $X \subset ℙ_{K}^{3}$ 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.

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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

Vol. 5, No. 3, 2023

Fabrizio Catanese and Matthias Schütt

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors