K3 surfaces of Picard rank one and degree two

  • Authors:

  • Andreas-Stephan Elsenhans;Jörg Jahnel

  • Affiliations:

  • Universität Göttingen, Mathematisches Institut, Göttingen, Germany;Universität Göttingen, Mathematisches Institut, Göttingen, Germany

  • Venue:
  • ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
  • Year:
  • 2008

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Abstract

We construct explicit examples of K3 surfaces over Q whichare of degree 2 and geometric Picard rank 1. We construct, particularly,examples of the form w2 = det M where M is a (3 × 3)-matrix of ternaryquadratic forms.