Vector fields, torus actions and equivariant cohomology

摘要

We give an explicit connection between the holomorphic equivariant cohomology as defined by Carrell and Lieberman and the usual equivariant cohomology of Borel and Cartan. Let X be a smooth complex projective variety equipped with a C*-action with fixed point set Z. By results of Carrell and Lieberman, there exists a filtration F-0 subset of F-1 subset of center dot center dot center dot of H* (Z, C) such that GrH* (Z, C) congruent to H* (X, C) as graded algebras. We give here an explicit connection between this filtration and the C*-equivariant cohomology of X.