The field of moduli of singular K3 surfaces
A singular K3 surface always admits a model over a number field. The absolute Galois group acts on the set of isomorphism classes of singular K3 surfaces, and it was proven by Schütt that the orbit of under this action is in 1:1 correspondence with the genus of the transcendental lattice of . In this talk, I will introduce the notion of field of -moduli, and I will study it in two cases:
1) is the CM field of ;
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.