2023/12/07 by Cécile Gachet, Gachet, Cécile, Zhining Liu +3
Mathematics · #14F35 #14M25 #20F34 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Primary 14E30 #Secondary 90C57
paper · pdf · doi:10.48550/arxiv.2312.03981
openalex publication_date 2023/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we study the orbifold fundamental group π1\rm orb(X,Δ) of a Calabi--Yau pair (X,Δ) with log canonical singularities. We conjecture that the orbifold fundamental group π1\rm orb(X,Δ) of a n-dimensional log Calabi--Yau pair admits a normal solvable subgroup of rank at most 2n and index at most c(n). We prove this conjecture in the case that n=2. More precisely, for a log Calabi--Yau surface pair (X,Δ) we show that π1\rm orb(X,Δ) is the extension of a nilpotent group of length at most 2 and rank at most 4 by a finite group of order at most 7200. We also show that the bounds on the nilpotency length, rank, and order of the finite group quotient in this result are sharp. Finally, we provide some necessary criteria for a log Calabi--Yau surface (X,Δ) to have an infinite, or a non virtually abelian orbifold fundamental group.