Affine hyperplane arrangements at finite distance

Anaëlle Pfister

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arXiv · 2602.00847

Affine hyperplane arrangements at finite distance

Anaëlle Pfister

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Abstract

We study the relative homology group of an affine hyperplane arrangement and its Poincar\'e dual, the cohomology at finite distance of the complement. We give an Orlik--Solomon-type description of the latter, and identify it with the vector space of logarithmic forms having vanishing residues at infinity. To this end, we introduce a partial version of wonderful compactifications, which could be relevant in other contexts where blow-ups only occur at infinity. Finally, we show that the cohomology at finite distance coincides with the vector space of canonical forms in the sense of positive geometry.

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BibTeX RIS

Anaëlle Pfister. 2026-01-31. Affine hyperplane arrangements at finite distance. https://arxiv.org/abs/2602.00847

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