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Abstract Laface

The field of moduli of singular K3 surfaces

A singular K3 surface X always admits a model over a number field. The absolute Galois group \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 X under this action is in 1:1 correspondence with the genus of the transcendental lattice of X. In this talk, I will introduce the notion of field of K-moduli, and I will study it in two cases:

1) K is the CM field of X;

2) 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.