The equivariant cohomology ring of regular varieties
| dc.creator | Brion, Michel | |
| dc.creator | Carrell, James B. | |
| dc.date | 2002-11-02 | |
| dc.date.accessioned | 2026-07-07T04:52:35Z | |
| dc.date.available | 2026-07-07T04:52:35Z | |
| dc.description | Let $B$ denote the upper triangular subgroup of $SL_2(C)$, $T$ its diagonal torus and $U$ its unipotent radical. A complex projective variety $Y$ endowed with an algebraic action of $B$ such that the fixed point set $Y^U$ is a single point, is called regular. Associated to any regular $B$-variety $Y$, there is a remarkable affine curve $Z_Y$ with a $T$-action which was studied by the second author. In this note, we show that the coordinate ring of $Z_Y$ is isomorphic with the equivariant cohomology ring $H_T^*(Y)$ with complex coefficients, when $Y$ is smooth or, more generally, is a $B$-stable subvariety of a regular smooth $B$-variety $X$ such that the restriction map from $H^*(X)$ to $H^*(Y)$ is surjective. This isomorphism is obtained as a refinement of the localization theorem in equivariant cohomology; it applies e.g. to Schubert varieties in flag varieties, and to the Peterson variety studied by Kostant. Another application of our isomorphism is a natural algebraic formula for the equivariant push forward. | |
| dc.description | LaTeX, 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0211026 | |
| dc.identifier | http://arxiv.org/abs/math/0211026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65519 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 14L30; 14M15; 55N91 | |
| dc.title | The equivariant cohomology ring of regular varieties | |
| dc.type | text |