Work

Fundamental groups of Calabi-Yau spaces

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.09269

Authors: Fu, Xin, Guo, Bin, Song, Jian, Wang, Juanyong

Institutions: Westlake University, Rutgers, The State University of New Jersey

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China

Awards: G1603846912, Differential Equations in Complex Riemannian Geometry, Analysis and PDEs in complex geometry, G6397008029, G8533620077

OpenAlex ID: W7221017781

Cites: 52

Cited by: 2

Related to: 10