Singularities of normal quartic surfaces II (char=2)

authored by

Fabrizio Catanese, Matthias Schütt

Abstract

We show, in this second part, that the maximal number of singular points of a quartic surface \(X \subset \mathbb{P}^3_K\) defined over an algebraically closed field \(K\) of characteristic \(2\) is at most \(14\), and that, if we have \(14\) singularities, these are nodes and moreover the minimal resolution of \(X\) is a supersingular K3 surface. We produce an irreducible component, of dimension \(24\), of the variety of quartics with \(14\) nodes. We also exhibit easy examples of quartics with \(7\) \(A_3\)-singularities.

Organisation(s)

Institut für Algebraische Geometrie
Riemann Center for Geometry and Physics

External Organisation(s)

Universität Bayreuth

Type

Artikel

Journal

Pure and Applied Mathematics Quarterly

Volume

18

Pages

1379-1420

No. of pages

42

ISSN

1558-8599

Publication date

25.10.2022

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Mathematik (insg.)

Electronic version(s)

https://arxiv.org/abs/2110.03078 (Access: Offen)
https://doi.org/10.4310/PAMQ.2022.v18.n4.a5 (Access: Geschlossen)