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arXiv · 2004.00522

The local fundamental group of a Kawamata log terminal singularity is finite

Lukas Braun
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Abstract

We prove a conjecture of Koll\'ar stating that the local fundamental group of a klt singularity $x$ is finite. In fact, we prove a stronger statement, namely that the fundamental group of the smooth locus of a neighbourhood of $x$ is finite. We call this the regional fundamental group. As the proof goes via a local-to-global induction, we simultaneously confirm finiteness of the orbifold fundamental group of the smooth locus of a weakly Fano pair.

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Lukas Braun. 2020-04-01. The local fundamental group of a Kawamata log terminal singularity is finite. https://doi.org/10.1007/s00222-021-01062-0

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