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# On the Spectrum of the Equivariant Cohomology Ring

Published:2009-12-04
Printed: Apr 2010
• Mark Goresky
• Robert MacPherson
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## Abstract

If an algebraic torus $T$ acts on a complex projective algebraic variety $X$, then the affine scheme $\operatorname{Spec} H^*_T(X;\mathbb C)$ associated with the equivariant cohomology is often an arrangement of linear subspaces of the vector space $H_2^T(X;\mathbb C).$ In many situations the ordinary cohomology ring of $X$ can be described in terms of this arrangement.
 MSC Classifications: 14L30 - Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 54H15 - Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]