The homology groups of finite cyclic covering of line arrangement complement
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912657871732736 |
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| author | Liu, Yongqiang Xie, Wentao |
| author_facet | Liu, Yongqiang Xie, Wentao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10939 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The homology groups of finite cyclic covering of line arrangement complement Liu, Yongqiang Xie, Wentao Algebraic Geometry Algebraic Topology 52C35, 32S55 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. |
| title | The homology groups of finite cyclic covering of line arrangement complement |
| topic | Algebraic Geometry Algebraic Topology 52C35, 32S55 |
| url | https://arxiv.org/abs/2312.10939 |