Homology of Local Systems on Real Line Arrangement Complements

Fuente: arXiv
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Main Authors: Xie, Baiting, Yu, Chenglong
Format: Preprint
Published: 2025
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_version_ 1866918470425247744
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