The field of moduli of singular K3 surfaces

Abstract

We study the field of moduli of singular abelian and K3 surfaces. We discuss both the field of moduli over the CM field and over $\Q$. We also discuss non-finiteness with respect to the degree of the field of moduli. Finally, we provide an explicit approach to the computation of the field of moduli.

arXiv comment22 pages. It has been pointed out that Proposition 6.1 in the previous version contained a gap, which we fix in this new and updated version. Incidentally, we also use this idea to improve our results on the absolute field. Title has changed. Comments are still welcome!