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On the Spectrum of the Equivariant Cohomology Ring

Published online by Cambridge University Press:  20 November 2018

Mark Goresky  and
Robert MacPherson
Mark Goresky
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, NJ, USA, e-mail: goresky@ias.edu, rdm@math.ias.edu
Robert MacPherson
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, NJ, USA, e-mail: goresky@ias.edu, rdm@math.ias.edu
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Abstract

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If an algebraic torus $T$ acts on a complex projective algebraic variety $X$, then the affine scheme $\text{Spec}\,H_{T}^{*}\left( X;\,\mathbb{C} \right)$ associated with the equivariant cohomology is often an arrangement of linear subspaces of the vector space $H_{2}^{T}\left( X;\,\mathbb{C} \right)$. In many situations the ordinary cohomology ring of $X$ can be described in terms of this arrangement.

Keywords

14L3054H15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 2 , 01 April 2010 , pp. 262 - 283
Copyright
Copyright © Canadian Mathematical Society 2010

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