Holomorphic Equivariant Cohomology via a Transversal Holomorphic Vector Field

Details Holomorphic Equivariant Cohomology via a Transversal Holomorphic Vector Field Holomorphic Equivariant Cohomology via a Transversal Holomorphic Vector Field

2003-04-15

arxiv.org/abs/math/0304200v2

Mathematics

Differential Geometry

18 pages. has been accepted by International Journal of Mathematics

Scientific paper

In this paper an analytic proof of a generalization of a theorem of Bismut ([Bis1, Theorem 5.1]) is given, which says that, when $v$ is a transversal holomorphic vector field on a compact complex manifold $X$ with a zero point set $Y$, the embedding $j:Y\to X$ induces a natural isomorphism between the holomorphic equivariant cohomology of $X$ via $v$ with coefficients in $\xi$ and the Dolbeault cohomology of $Y$ with coefficients in $\xi|_Y$, where $\xi\to X$ is a holomorphic vector bundle over $X$.

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