Galois embedding of K3 surface --abelian case--

TL;DR

This paper investigates Galois embeddings of K3 surfaces with abelian Galois groups, revealing specific group structures and geometric properties of the surfaces involved.

Contribution

It characterizes possible abelian Galois groups and describes the structure of K3 surfaces admitting such embeddings, including their realization as complete intersections.

Findings

Galois group is isomorphic to Z/4Z, Z/6Z, or Z/2Z⊕Z/2Z⊕Z/2Z

K3 surfaces are smooth complete intersections of hypersurfaces

Detailed structure of these Galois embeddings is provided

Abstract

We study Glois embeddings of K3 surfaces in the case where the Galois groups are abelian. We show several properties of K3 surfaces concerning the Galois embeddings. In particular, if the Galois group G is abelian, then G is isomorphic to Z/4Z, Z/6Z or Z/2Z\oplusZ/2Z\oplusZ/2Z and S is a smooth complete intersection of hypersurfaces. Further, we state the detailed structure of such surfaces.