Finite subgroups of automorphisms of K3 surfaces
Algebraic Geometry
2023-03-27 v4
Abstract
We give a complete classification of finite subgroups of automorphisms of K3 surfaces up to deformation. The classification is in terms of Hodge theoretic data associated to certain conjugacy classes of finite subgroups of the orthogonal group of the K3 lattice. The moduli theory of K3 surfaces, in particular the surjectivity of the period map and the strong Torelli theorem allow us to interpret this datum geometrically. Our approach is computer aided and involves hermitian lattices over number fields.
Keywords
Cite
@article{arxiv.2112.07715,
title = {Finite subgroups of automorphisms of K3 surfaces},
author = {Simon Brandhorst and Tommy Hofmann},
journal= {arXiv preprint arXiv:2112.07715},
year = {2023}
}
Comments
52 pages, for ancillary files see https://doi.org/10.5281/zenodo.6544475