Finite abelian groups acting on rationally connected threefolds II: groups of K3 type
Algebraic Geometry
2026-02-24 v2
Abstract
We study finite abelian groups acting on three-dimensional rationally connected varieties. We concentrate on the groups of K3 type, that is, abelian extensions by a cyclic group of groups that faithfully act on a K3 surface. In particular, if a finite abelian group faithfully acts on a threefold preserving a K3 surface (with at worst du Val singularities), then such a group is of K3 type. We prove a classification theorem for the groups of K3 type which can act on three-dimensional rationally connected varieties. We note the relation between certain groups of K3 type and K3 surfaces with higher Picard number.
Keywords
Cite
@article{arxiv.2509.02531,
title = {Finite abelian groups acting on rationally connected threefolds II: groups of K3 type},
author = {Konstantin Loginov and Antoine Pinardin and Zhijia Zhang},
journal= {arXiv preprint arXiv:2509.02531},
year = {2026}
}