TY - JOUR

T1 - Singularities of normal quartic surfaces II (char=2)

AU - Catanese, Fabrizio

AU - Schütt, Matthias

N1 - Publisher Copyright: © 2022, International Press, Inc.. All rights reserved.

PY - 2022/10/25

Y1 - 2022/10/25

N2 - 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.

AB - 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.

KW - Gauss map

KW - genus one fibration

KW - Quartic surface

KW - singularity

KW - supersingular K3 surface

UR - http://www.scopus.com/inward/record.url?scp=85140387444&partnerID=8YFLogxK

U2 - 10.4310/PAMQ.2022.v18.n4.a5

DO - 10.4310/PAMQ.2022.v18.n4.a5

M3 - Article

VL - 18

SP - 1379

EP - 1420

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

SN - 1558-8599

IS - 4

ER -