Holomorphic Morse Inequalities and Symplectic Reduction

Details Holomorphic Morse Inequalities and Symplectic Reduction Holomorphic Morse Inequalities and Symplectic Reduction

1997-05-02

arxiv.org/abs/dg-ga/9705002v2

Mathematics

Differential Geometry

LaTeX 2e, 9 pages

Scientific paper

We introduce Morse-type inequalities for a holomorphic circle action on a holomorphic vector bundle over a compact Kaehler manifold. Our inequalities produce bounds on the multiplicities of weights occurring in the twisted Dolbeault cohomology in terms of the data of the fixed points and of the symplectic reduction. This result generalizes both Wu-Zhang extension of Witten's holomorphic Morse inequalities and Tian-Zhang Morse-type inequalities for symplectic reduction. As an application we get a new proof of the Tian-Zhang relative index theorem for symplectic quotients.

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