# Abstract Laface

The field of moduli of singular K3 surfaces

A singular K3 surface $\dpi{300}\inline X$ always admits a model over a number field. The absolute Galois group $\dpi{300}\inline \text{Gal}(\mathbb{C} / \mathbb{Q})$ acts on the set of isomorphism classes of singular K3 surfaces, and it was proven by Schütt that the orbit of $\dpi{300}\inline X$ under this action is in 1:1 correspondence with the genus of the transcendental lattice of $\dpi{300}\inline X$. In this talk, I will introduce the notion of field of $\dpi{300}\inline K$-moduli, and I will study it in two cases:

1) $\dpi{300}\inline K$ is the CM field of $\dpi{300}\inline X$;

2) $\dpi{300}\inline K = \mathbb{Q}$ .

Differences and analogies of these two settings will be highlighted. Furthermore, I will illustrate how the field of moduli varies within the moduli space of singular K3 surface. Time permitting, I will discuss some computation-oriented aspects.