Complex Multiplication for K3 Surfaces

Details Complex Multiplication for K3 Surfaces Complex Multiplication for K3 Surfaces

2005-07-31

arxiv.org/abs/math/0508018v1

Mathematics

Algebraic Geometry

30 pages, LaTeX

Scientific paper

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 $\Q$, constructed using algebraic stacks, to the canonical model of the Shimura variety associated to $\SO(2,19)$.

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