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# Goresky—MacPherson Calculus for the Affine Flag Varieties

Published:2009-12-04
Printed: Apr 2010
• Zhiwei Yun
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## Abstract

We use the fixed point arrangement technique developed by Goresky and MacPherson to calculate the part of the equivariant cohomology of the affine flag variety $\mathcal{F}\ell_G$ generated by degree 2. We use this result to show that the vertices of the moment map image of $\mathcal{F}\ell_G$ lie on a paraboloid.
 MSC Classifications: 14L30 - Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 55N91 - Equivariant homology and cohomology [See also 19L47]