Fundamental Groups and Coregularity: Klt Pairs with Trivial and Nef Log-Anticanonical Class
Abstract
In this article, we study how the absolute coregularity of a projective log pair reflects on its fundamental group. More precisely, we show that for a projective klt log pair (X,D) of absolute coregularity c and arbitrary dimension the fundamental group π1reg(X,D) admits a normal abelian subgroup of finite index and rank at most 2c. We reduce this statement to klt Calabi-Yau pairs with standard coefficients of dimension c. In the cases 0≤ c≤2 and fixed dimension, we can furthermore bound the index of a solvable normal subgroup. Combining the reduction with the recent regular-locus theorem of Fu-Guo-Song-Wang, we prove the coregularity bound in every dimension. In particular, for a projective klt pair (X,D) with −(KX+D) nef, the orbifold fundamental group of the smooth locus is virtually abelian of rank at most 2 dimX.
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BibTeX
@misc{braun2026fundamental,
title = {{Fundamental Groups and Coregularity: Klt Pairs with Trivial and Nef Log-Anticanonical Class}},
author = {Lukas Braun and Fernando Figueroa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21358},
eprint = {2610.21358},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21358},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fundamental Groups and Coregularity: Klt Pairs with Trivial and Nef Log-Anticanonical Class
AU - Lukas Braun
AU - Fernando Figueroa
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21358
UR - https://arxiv.org/abs/2610.21358
AB - In this article, we study how the absolute coregularity of a projective log pair reflects on its fundamental group. More precisely, we show that for a projective klt log pair (X,D) of absolute coregularity c and arbitrary dimension the fundamental group π_1^reg(X,D) admits a normal abelian subgroup of finite index and rank at most 2c. We reduce this statement to klt Calabi-Yau pairs with standard coefficients of dimension c. In the cases 0≤ c≤2 and fixed dimension, we can furthermore bound the index of a solvable normal subgroup. Combining the reduction with the recent regular-locus theorem of Fu-Guo-Song-Wang, we prove the coregularity bound in every dimension. In particular, for a projective klt pair (X,D) with −(K_X+D) nef, the orbifold fundamental group of the smooth locus is virtually abelian of rank at most 2 dimX.
ER -