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K3 Surfaces of Picard Rank One and Degree Two

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Algorithmic Number Theory (ANTS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5011))

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Abstract

We construct explicit examples of K3 surfaces over  which are of degree 2 and geometric Picard rank 1. We construct, particularly, examples of the form \(w^2 = \det M\) where M is a (3 ×3)-matrix of ternary quadratic forms.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Göttingen, Bunsenstraße 3–5, D-37073, Göttingen, Germany

    Andreas-Stephan Elsenhans & Jörg Jahnel

Authors
  1. Andreas-Stephan Elsenhans
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  2. Jörg Jahnel
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Alfred J. van der Poorten Andreas Stein

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Elsenhans, AS., Jahnel, J. (2008). K3 Surfaces of Picard Rank One and Degree Two. In: van der Poorten, A.J., Stein, A. (eds) Algorithmic Number Theory. ANTS 2008. Lecture Notes in Computer Science, vol 5011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79456-1_14

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  • DOI: https://doi.org/10.1007/978-3-540-79456-1_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79455-4

  • Online ISBN: 978-3-540-79456-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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