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arXiv · 2512.21531

Homology of Local Systems on Real Line Arrangement Complements

Baiting Xie·Chenglong Yu
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Abstract

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.

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Baiting Xie, Chenglong Yu. 2025-12-25. Homology of Local Systems on Real Line Arrangement Complements. https://arxiv.org/abs/2512.21531

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