English

Real multiplication on K3 surfaces and Kuga Satake varieties

Algebraic Geometry 2007-05-23 v1

Abstract

The endomorphism algebra of a K3 type Hodge structure is a totally real field or a CM field. In this paper we give a low brow introduction to the case of a totally real field. We give existence results for the Hodge structures, for their polarizations and for certain K3 surfaces. We consider the Kuga Satake variety of these Hodge structures and we discuss some examples. Finally we indicate various open problems related to the Hodge conjecture.

Keywords

Cite

@article{arxiv.math/0609839,
  title  = {Real multiplication on K3 surfaces and Kuga Satake varieties},
  author = {Bert van Geemen},
  journal= {arXiv preprint arXiv:math/0609839},
  year   = {2007}
}
R2 v1 2026-07-22T17:43:18.051Z