Determinantal quartics and the computation of the Picard group

2010/10/10 by Andreas-Stephan Elsenhans, Elsenhans, Andreas-Stephan, Jörg Jahnel +1
Mathematics · #14J27 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary 14J28 #Secondary 14C22 #math.AG #math.NT #msc:14C22 #msc:14J27 #msc:14J28

paper · pdf · doi:10.48550/arxiv.1010.1923

arxiv created 2010/10/10 · arxiv updated 2010/10/12

Abstract

We test the methods for computing the Picard group of a K3 surface in a situation of high rank. The examples chosen are resolutions of quartics in \bP³ having 14 singularities of type A₁. Our computations show that the method of R. van Luijk works well when sufficiently large primes are used.

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