English

On the component group of the algebraic monodromy group of a $K3$ surface

Algebraic Geometry 2024-02-15 v2

Abstract

We provide a lower bound for the number of components of the algebraic monodromy group in the situation of a K3K3 surface over a number field kk. In the CM case, our bound is sharp. As an application, we describe, in the case of CM, the jump character \cite[Definition~2.4.6]{CEJ} entirely in terms of the endomorphism field and the geometric Picard rank.

Keywords

Cite

@article{arxiv.2304.07585,
  title  = {On the component group of the algebraic monodromy group of a $K3$ surface},
  author = {Andreas-Stephan Elsenhans and Jörg Jahnel},
  journal= {arXiv preprint arXiv:2304.07585},
  year   = {2024}
}