Virtually abelian symmetry groups of hyperbolic lattices
Algebraic Geometry
2025-07-29 v1 Number Theory
Abstract
We give a classification of integral lattices with virtually abelian symmetry group. As a consequence, we complete the classification of K3 surfaces with virtually abelian automorphism group. In the appendix we formulate an algorithm for weak approximation in orthogonal groups and use it to determine if two indefinite lattices are isometric.
Keywords
Cite
@article{arxiv.2507.20743,
title = {Virtually abelian symmetry groups of hyperbolic lattices},
author = {Simon Brandhorst and Markus Kirschmer and Giacomo Mezzedimi},
journal= {arXiv preprint arXiv:2507.20743},
year = {2025}
}
Comments
14 pages; with an appendix by Simon Brandhorst and Markus Kirschmer