Volume 22, issue 3 (2022)

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Equivariant cohomology and the super reciprocal plane of a hyperplane arrangement

Sophie Kriz

Algebraic & Geometric Topology 22 (2022) 991–1015
Abstract

We investigate certain graded-commutative rings which are related to the reciprocal plane compactification of the coordinate ring of a complement of a hyperplane arrangement. We give a presentation of these rings by generators and defining relations. This presentation was used by Holler and I Kriz (2020) to calculate the –graded coefficients of localizations of ordinary  RO((p)n)–graded equivariant cohomology at a given set of representation spheres, and also more recently by the author in a generalization to the case of an arbitrary finite group. We also give an interpretation of these rings in terms of superschemes, which can be used to further illuminate their structure.

Keywords
equivariant cohomology, hyperplane arrangements, superschemes
Mathematical Subject Classification 2010
Primary: 05E40, 52C35, 55N91
References
Publication
Received: 25 September 2016
Revised: 5 May 2021
Accepted: 19 May 2021
Published: 25 August 2022
Authors
Sophie Kriz
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States