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Equivariant Holomorphic Morse Inequalities III: Non-Isolated Fixed Points

Siye Wu·Weiping Zhang
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Abstract

We prove the equivariant holomorphic Morse inequalities for a holomorphic torus action on a holomorphic vector bundle over a compact Kahler manifold when the fixed-point set is not necessarily discrete. Such inequalities bound the twisted Dolbeault cohomologies of the Kahler manifold in terms of those of the fixed-point set. We apply the inequalities to obtain relations of Hodge numbers of the connected components of the fixed-point set and the whole manifold. We also investigate the consequences in geometric quantization, especially in the context of symplectic cutting.

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BibTeXRIS

Siye Wu, Weiping Zhang. 1997-01-24. Equivariant Holomorphic Morse Inequalities III: Non-Isolated Fixed Points. https://arxiv.org/abs/dg-ga/9701009

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