Cohomology of the Mumford Quotient
| dc.creator | Braverman, Maxim | |
| dc.date | 1998-09-24 | |
| dc.date | 2000-11-08 | |
| dc.date.accessioned | 2026-07-07T05:26:09Z | |
| dc.date.available | 2026-07-07T05:26:09Z | |
| dc.description | 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. | |
| dc.description | 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" | |
| dc.identifier | https://arxiv.org/abs/math/9809146 | |
| dc.identifier | http://arxiv.org/abs/math/9809146 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77443 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.title | Cohomology of the Mumford Quotient | |
| dc.type | text |