The Jordan property for local fundamental groups

Abstract

We show the Jordan property for regional fundamental groups of klt singularities of fixed dimension. Furthermore, we prove the existence of effective simultaneous index one covers for $n$-dimensional klt singularities. We give an application to the study of local class groups of klt singularities.

arXiv commentComments are welcome. v2: final accepted version. To appear in Geometry & Topology. Only minor changes, corrected typos, updated bibliography. 24 pages; v1: 24 pages

References in corpus (9)

• Finiteness of algebraic fundamental groups
• Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties
• Jordan property for groups of birational selfmaps
• Locally nilpotent derivations on affine surfaces with a $\C^*$-action
• ACC for minimal log discrepancies of exceptional singularities
• New examples of terminal and log canonical singularities
• Finiteness of fundamental groups
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Cited by in corpus (7)

• Kawamata log terminal singularities of full rank
• Iteration of Cox rings of klt singularities
• Reductive quotients of klt singularities
• A geometric characterization of toric singularities
• Finite groups of birational transformations
• Symmetries of Fano varieties
• On termination of flips and fundamental groups