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.

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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)