The Picard Group of Various Families of\n (\ℤ/2\ℤ)⁴-invariant Quartic K3 Surfaces

2015/11/05 by Florian Bouyer, Bouyer, Florian
Computer Science · Mathematics · #14C22 #14J28 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1511.01781

openalex publication_date 2015/11/05 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

The subject of this paper is the study of various families of quartic K3\nsurfaces which are invariant under a certain (\ℤ/2\ℤ)⁴\naction. In particular, we describe families whose general member contains\n8,16,24 or 32 lines as well as the 320 conics found by Eklund (some of\nwhich degenerate into the mentioned lines). The second half of this paper is\ndedicated to finding the Picard group of a general member of each of these\nfamilies, and describing it as a lattice. It turns out that for each family the\nPicard group of a very general surface is generated by the lines and conics\nlying on said surface.\n

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