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

Abstract

We prove a conjecture of Kollár 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.

minor corrections, added Corollary 5 and some references

References in corpus (3)

• New examples of terminal and log canonical singularities
• Finiteness of étale fundamental groups by reduction modulo $p$
• Étale Covers and Local Algebraic Fundamental Groups

Cited by in corpus (9)

• The Jordan property for local fundamental groups
• Uniqueness of the minimizer of the normalized volume function
• Projective flatness over klt spaces and uniformisation of varieties with nef anti-canonical divisor
• Iteration of Cox rings of klt singularities
• Kawamata log terminal singularities of full rank
• Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs
• A decomposition theorem for $\mathbb{Q}$-Fano Kähler-Einstein varieties
• Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities
• On termination of flips and fundamental groups