Homology of Local Systems on Real Line Arrangement Complements
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918470425247744 |
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| author | Xie, Baiting Yu, Chenglong |
| author_facet | Xie, Baiting Yu, Chenglong |
| contents | We study the homology groups of the complement of a complexified real line arrangement with coefficients in complex rank-one local systems. Using Borel--Moore homology, we establish an algorithm computing their dimensions via the real figures of the arrangement. It enables us to give a new upper bound. We further consider the case where the arrangement contains a sharp pair and make partial progress on a conjecture proposed by Yoshinaga. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homology of Local Systems on Real Line Arrangement Complements Xie, Baiting Yu, Chenglong Algebraic Geometry 32S22 (Primary) 14N20, 52C35, 55N25 (Secondary) We study the homology groups of the complement of a complexified real line arrangement with coefficients in complex rank-one local systems. Using Borel--Moore homology, we establish an algorithm computing their dimensions via the real figures of the arrangement. It enables us to give a new upper bound. We further consider the case where the arrangement contains a sharp pair and make partial progress on a conjecture proposed by Yoshinaga. |
| title | Homology of Local Systems on Real Line Arrangement Complements |
| topic | Algebraic Geometry 32S22 (Primary) 14N20, 52C35, 55N25 (Secondary) |
| url | https://arxiv.org/abs/2512.21531 |