Some remarks on Brauer groups of K3 surfaces

Bert van Geemen

Some remarks on Brauer groups of K3 surfaces

Algebraic Geometry 2007-05-23 v2

Authors: Bert van Geemen

Abstract

We discuss the geometry of the genus one fibrations associated to an elliptic fibration on a K3 surface. We show that the two-torsion subgroup of the Brauer group of a general elliptic fibration is naturally isomorphic to the two-torsion of the Jacobian of a curve associated to the fibration. We remark that this is related to Recillas' trigonal construction. Finally we discuss the two-torsion in the Brauer group of a general K3 surface with a polarisation of degree two.

Keywords

algebraic surfaces fibrations brauer algebras

Cite

@article{arxiv.math/0408006,
  title  = {Some remarks on Brauer groups of K3 surfaces},
  author = {Bert van Geemen},
  journal= {arXiv preprint arXiv:math/0408006},
  year   = {2007}
}

Comments

This replacement has a more general theorem (thm 6.2) on Brauer groups of double covers of rational surfaces. Corrected some typos, updated references. To appear in Advances in Mathematics

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