Singularities of normal quartic surfaces II (char=2)

2021/10/06 by Fabrizio Catanese, Matthias Schütt, Catanese, Fabrizio +1
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2110.03078

Abstract

We show, in this second part, that the maximal number of singular points of a quartic surface X ⊂ ℙ³_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 A₃-singularities.

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