On the equivariant cohomology of subvarieties of a B-regular variety

Details On the equivariant cohomology of subvarieties of a B-regular variety On the equivariant cohomology of subvarieties of a B-regular variety

2008-09-06

arxiv.org/abs/0809.1136v1

Mathematics

Algebraic Geometry

12 pages, LaTeX. To appear in Transformation Groups

Scientific paper

By a $B$-regular variety, we mean a smooth projective variety over $C$ admitting an algebraic action of the upper triangular Borel subgroup $B \subset SL_2(C)$ such that the unipotent radical in $B$ has a unique fixed point. A result of M. Brion and the first author describes the equivariant cohomology algebra (over $C$) of a $B$-regular variety $X$ as the coordinate ring of a remarkable affine curve in $X \times P^1$. The main result of this paper uses this fact to classify the $B$-invariant subvarieties $Y$ of a $B$-regular variety $X$ for which the restriction map $i_Y:H^*(X) \to H^*(Y)$ is surjective.

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