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Equivariant Holomorphic Morse Inequalities I: A Heat Kernel Proof

Varghese Mathai·Siye Wu
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Abstract

Assume that the circle group acts holomorphically on a compact Kähler 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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BibTeXRIS

Varghese Mathai, Siye Wu. 1996-03-26. Equivariant Holomorphic Morse Inequalities I: A Heat Kernel Proof. https://arxiv.org/abs/dg-ga/9602007

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