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arXiv · 2312.10939

The homology groups of finite cyclic covering of line arrangement complement

Yongqiang Liu·Wentao Xie
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Abstract

In this paper, we study the first homology group of finite cyclic covering of complex line arrangement complement. We show that this first integral homology group is torsion-free under certain condition similar to the one used by Cohen-Dimca-Orlik. In particular, this includes the case of the Milnor fiber, which generalizes the previous results obtained by Williams for complexified line arrangement to any complex line arrangement.

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Yongqiang Liu, Wentao Xie. 2023-12-18. The homology groups of finite cyclic covering of line arrangement complement. https://doi.org/10.1016/j.topol.2025.109633

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