Equivariant Holomorphic Morse Inequalities I: A Heat Kernel Proof

Details Equivariant Holomorphic Morse Inequalities I: A Heat Kernel Proof Equivariant Holomorphic Morse Inequalities I: A Heat Kernel Proof

1996-02-15

arxiv.org/abs/dg-ga/9602007v2

Mathematics

Algebraic Geometry

plain LaTeX, 15 pages, typos corrected and other minor modifications

Scientific paper

Assume that the circle group acts holomorphically on a compact K\"ahler manifold with isolated fixed points and that the action can be lifted holomorphically to a holomorphic Hermitian vector bundle. We give a heat kernel proof of the equivariant holomorphic Morse inequalities. We use some techniques developed by Bismut and Lebeau. These inequalities, first obtained by Witten using a different argument, produce bounds on the multiplicities of weights occurring in the twisted Dolbeault cohomologies in terms of the data of the fixed points.

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