1998/09/24 by Maxim Braverman, Braverman, Maxim · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.math/9809146
A mistake in the proof of Theorem 3.1.b is corrected. The definition of the integration map is slightly changed. To appear in "Quantization of singular symplectic quotients"
openalex publication_date 1998/09/24 · arxiv created 2000/11/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a smooth projective variety acted on by a reductive group G. Let L be a positive G-equivariant line bundle over X. We use the Witten deformation of the Dolbeault complex of L to show, that the cohomology of the sheaf of holomorphic sections of the induced bundle on the Mumford quotient of (X,L) is equal to the G-invariant part on the cohomology of the sheaf of holomorphic sections of L. This result, which was recently proven by C. Teleman by a completely different method, generalizes a theorem of Guillemin and Sternberg, which addressed the global sections. It also shows, that the Morse-type inequalities of Tian and Zhang for symplectic reduction are, in fact, equalities.