Determinantal quartics and the computation of the Picard group

Details Determinantal quartics and the computation of the Picard group Determinantal quartics and the computation of the Picard group

2010-10-10

arxiv.org/abs/1010.1923v1

Mathematics

Algebraic Geometry

Scientific paper

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
$\bP^3$ having 14 singularities of type $A_1$. Our computations show that the
method of R. van Luijk works well when sufficiently large primes are used.

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