The Hodge conjecture for self-products of certain K3 surfaces

Ulrich Schlickewei

The Hodge conjecture for self-products of certain K3 surfaces

Algebraic Geometry 2009-07-16 v1

Authors: Ulrich Schlickewei

Abstract

We use a result of van Geemen to determine the endomorphism algebra of the Kuga--Satake variety of a K3 surface with real multiplication. This is applied to prove the Hodge conjecture for self-products of double covers of $\PP^2$ which are ramified along six lines.

Keywords

Hodge conjecture K3 surfaces self-products Kuga-Satake variety real multiplication double covers endomorphism algebra

Cite

@article{arxiv.0907.2503,
  title  = {The Hodge conjecture for self-products of certain K3 surfaces},
  author = {Ulrich Schlickewei},
  journal= {arXiv preprint arXiv:0907.2503},
  year   = {2009}
}

Comments

24 pages

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