Equivariant cohomology and the super reciprocal plane of a hyperplane arrangement

Kriz, Sophie

doi:10.2140/agt.2022.22.991

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Equivariant cohomology and the super reciprocal plane of a hyperplane arrangement

Sophie Kriz

Algebraic & Geometric Topology 22 (2022) 991–1015

DOI: 10.2140/agt.2022.22.991

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 $ℤ$ –graded coefficients of localizations of ordinary $RO ({(ℤ ∕ p)}^{n})$ –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

Volume 22, issue 3 (2022)