Fundamental groups, coregularity, and low dimensional klt Calabi-Yau pairs

2024/01/02 by Lukas Braun, Braun, Lukas, Fernando Figueroa +1 · 1 citation
Mathematics · #14E30 #14F35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2401.01315

openalex publication_date 2024/01/02 · openalex created_date 2024/01/04 · openalex updated_date 2026/07/28

Abstract

In this article, we study how the absolute coregularity of a projective log pair reflects on its fundamental group. More precisely, we conjecture that for a projective klt log pair (X,D) of absolute coregularity c (and arbitrary dimension) the fundamental group π₁^{\rm reg}(X,D) admits a normal abelian subgroup of finite index and rank at most 2c. We prove this conjecture in the cases 0 ≤ c ≤ 3, building on the almost abelianity of the fundamental groups of klt Calabi-Yau pairs of dimension ≤ 3. In the cases c ∈ \0,1,2\ and fixed dimension, we can furthermore bound the index of a solvable normal subgroup. In dimension three, we are able to prove almost abelianity of the fundamental group of the regular locus for projective klt Calabi-Yau pairs.

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• Beauville-Bogomolov decomposition for klt varieties

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