Publications at the Riemann Center

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