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 compar- ing arrangements in different abelian groups. Our work is based on the Varchenko–Gel’fand ring for real hyper- plane arrangements and from that we deduce the coho- mology 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.
Bazzocchi, E., Pagaria, R., Pismataro, M. (2025). Cohomology ring of non‐compact abelian arrangements. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 131(6), 1-25 [10.1112/plms.70113].
Cohomology ring of non‐compact abelian arrangements
Bazzocchi, E.;Pagaria, R.
;Pismataro, M.
2025
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 compar- ing arrangements in different abelian groups. Our work is based on the Varchenko–Gel’fand ring for real hyper- plane arrangements and from that we deduce the coho- mology 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.| File | Dimensione | Formato | |
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