Details
| Original language | English |
|---|---|
| Pages (from-to) | 1379-1420 |
| Number of pages | 42 |
| Journal | Pure and Applied Mathematics Quarterly |
| Volume | 18 |
| Issue number | 4 |
| Publication status | Published - 25 Oct 2022 |
Abstract
Keywords
- Gauss map, genus one fibration, Quartic surface, singularity, supersingular K3 surface
ASJC Scopus subject areas
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In: Pure and Applied Mathematics Quarterly, Vol. 18, No. 4, 25.10.2022, p. 1379-1420.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Singularities of normal quartic surfaces II (char=2)
AU - Catanese, Fabrizio
AU - Schütt, Matthias
N1 - Funding Information: arXiv: 2110.03078 Received October 6, 2021. 2010 Mathematics Subject Classification: Primary 14J17, 14J28; secondary 14J25, 14N05. ∗The first author acknowledges support of the ERC 2013 Advanced Research Grant – 340258 – TADMICAMT.
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 -