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 surface over a number field . 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}
}