English

Complex Multiplication for K3 Surfaces

Algebraic Geometry 2007-05-23 v1 Number Theory

Abstract

In this note we prove analogues of the main theorems of complex multiplication for abelian varieties for K3 surfaces. This is done by studying the field of definition of the period morphism for complex K3 surfaces. More precisely we relate the moduli spaces of primitively polarized K3 surfaces with level structures over \Q\Q, constructed using algebraic stacks, to the canonical model of the Shimura variety associated to \SO(2,19)\SO(2,19).

Keywords

Cite

@article{arxiv.math/0508018,
  title  = {Complex Multiplication for K3 Surfaces},
  author = {Jordan Rizov},
  journal= {arXiv preprint arXiv:math/0508018},
  year   = {2007}
}

Comments

30 pages, LaTeX