Holomorphic Morse inequalities and symplectic reduction

DOI10.1016/S0040-9383(97)00105-5zbMATH Open0936.58009arXivdg-ga/9705002OpenAlexW2030945892MaRDI QIDQ1292665

Maxim Braverman

Publication date: 14 May 2000

Published in: Topology (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/dg-ga/9705002

zbMATH Keywords

fixed pointsholomorphic vector bundlesymplectic reductioncompact Kähler manifoldmultiplicities of weightsholomorphic circle actionMorse-type inequalitiesTian-Zhang relative index theoremtwisted Dolbeault cohomology

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10)

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