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Fundamental groups of Calabi-Yau spaces
Abstract
We study the fundamental groups of a normal projective Calabi-Yau variety X with klt singularities and of its regular locus Xreg. We prove that both groups are almost abelian, and that their ranks are determined by the irregularities of finite etale and quasi-etale covers, respectively. Our approach is differential geometric, and relies on recent advances in the geometric theory of complex Monge-Ampere equations.
Related
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BibTeX
@misc{fu2026fundamental,
title = {{Fundamental groups of Calabi-Yau spaces}},
author = {Xin Fu and Bin Guo and Jian Song and Juanyong Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09269},
eprint = {2610.09269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09269},
}
RIS
TY - UNPB
TI - Fundamental groups of Calabi-Yau spaces
AU - Xin Fu
AU - Bin Guo
AU - Jian Song
AU - Juanyong Wang
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09269
UR - https://arxiv.org/abs/2610.09269
AB - We study the fundamental groups of a normal projective Calabi-Yau variety X with klt singularities and of its regular locus X_reg. We prove that both groups are almost abelian, and that their ranks are determined by the irregularities of finite etale and quasi-etale covers, respectively. Our approach is differential geometric, and relies on recent advances in the geometric theory of complex Monge-Ampere equations.
ER -