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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 63, Issue 2 (Apr 2013)

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On the computation of the Picard group for certain singular quartic surfaces

Andreas-Stephan Elsenhans / Jörg Jahnel
Published Online: 2013-03-28 | DOI: https://doi.org/10.2478/s12175-012-0094-x

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 P 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.

MSC: Primary 14J28; Secondary 14C22, 14J27

Keywords: K3 surface; singular quartic surface; Cayley-Rohn quartic; A1 singularity; Picard rank; van Luijk’s method

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About the article

Published Online: 2013-03-28

Published in Print: 2013-04-01


Citation Information: Mathematica Slovaca, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-012-0094-x.

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© 2013 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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Andreas-Stephan Elsenhans and Jörg Jahnel
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