1997/05/02 by Maxim Braverman, Braverman, Maxim
Mathematics · #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #dg-ga #math.DG
paper · pdf · doi:10.48550/arxiv.dg-ga/9705002
LaTeX 2e, 9 pages
openalex publication_date 1997/05/02 · arxiv created 1997/05/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.