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

• 成果类型: Article
• 署名作者: Braun, Lukas
• 署名单位: University of Freiburg
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01062-0
• 发表日期: 2021
• 页码: 845-896
• 关键词: kahler-einstein metrics; simple connectedness; orbifolds; CLASSIFICATION; VARIETIES; sheaves

摘要

We prove a conjecture of Kollar 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.