Vanishing theorems for the kernel of a Dirac operator
| dc.creator | Braverman, Maxim | |
| dc.date | 1998-05-27 | |
| dc.date | 1998-09-24 | |
| dc.date.accessioned | 2026-07-07T05:24:52Z | |
| dc.date.available | 2026-07-07T05:24:52Z | |
| dc.description | We obtain a vanishing theorem for the kernel of a Dirac operator on a Clifford module twisted by a sufficiently large power of a line bundle, whose curvature is non-degenerate at any point of the base manifold. In particular, if the base manifold is almost complex, we prove a vanishing theorem for the kernel of a $\spin^c$ Dirac operator twisted by a line bundle with curvature of a mixed sign. In this case we also relax the assumption of non-degeneracy of the curvature. These results are generalization of a vanishing theorem of Borthwick and Uribe. As an application we obtain a new proof of the classical Andreotti-Grauert vanishing theorem for the cohomology of a compact complex manifold with values in the sheaf of holomorphic sections of a holomorphic vector bundle, twisted by a large power of a holomorphic line bundle with curvature of a mixed sign. As another application we calculate the sign of the index of a signature operator twisted by a large power of a line bundle. | |
| dc.description | A mistake in Theorem 3.13 is corrected. Some othe misprints are removed | |
| dc.identifier | https://arxiv.org/abs/math/9805127 | |
| dc.identifier | http://arxiv.org/abs/math/9805127 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76973 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32L20 (primary) ; 58G10, 14F17 (secondary) | |
| dc.title | Vanishing theorems for the kernel of a Dirac operator | |
| dc.type | text |