Finite abelian groups acting on rationally connected threefolds II: groups of K3 type

Fuente: arXiv
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Main Authors: Loginov, Konstantin, Pinardin, Antoine, Zhang, Zhijia
Format: Preprint
Published: 2025
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author Loginov, Konstantin
Pinardin, Antoine
Zhang, Zhijia
author_facet Loginov, Konstantin
Pinardin, Antoine
Zhang, Zhijia
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_02531
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Finite abelian groups acting on rationally connected threefolds II: groups of K3 type
Loginov, Konstantin
Pinardin, Antoine
Zhang, Zhijia
Algebraic Geometry
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.
title Finite abelian groups acting on rationally connected threefolds II: groups of K3 type
topic Algebraic Geometry
url https://arxiv.org/abs/2509.02531