Non-projective K3 surfaces with real or Salem multiplication
Algebraic Geometry
2025-11-26 v1 Complex Variables
Dynamical Systems
Number Theory
Abstract
We determine the Hodge endomorphism algebras of non-projective complex K3 surfaces (and more generally, hyperk\"ahler manifolds). We show that they are either totally real fields or number fields generated by Salem numbers. This is unlike the projective case, where the endomorphism fields are either totally real or CM. We also develop precise existence criteria and explore the relations to number theory and dynamics.
Cite
@article{arxiv.2511.19970,
title = {Non-projective K3 surfaces with real or Salem multiplication},
author = {Eva Bayer-Fluckiger and Bert van Geemen and Matthias Schütt},
journal= {arXiv preprint arXiv:2511.19970},
year = {2025}
}
Comments
44 pages