Year: 2025
Type: article
Abstract: We give an Orlik–Solomon‐type presentation for the cohomology ring of arrangements in a non‐compact abelian Lie group. The new insight consists of comparing arrangements in different abelian groups. Our work is based on the Varchenko–Gel'fand ring for real hyperplane arrangements and from that we deduce the cohomology rings of all other abelian arrangements. As a by‐product, we obtain a new proof of the Orlik–Solomon relations and those of De Concini–Procesi.
DOI: 10.1112/plms.70113
Authors: E. Bazzocchi, R. Pagaria, M. Pismataro
Institution: University of Bologna
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417434740