Bergman kernels and equilibrium measures for ample line bundles
| dc.creator | Berman, Robert | |
| dc.date | 2007-04-12 | |
| dc.date.accessioned | 2026-07-07T07:56:22Z | |
| dc.date.available | 2026-07-07T07:56:22Z | |
| dc.description | Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power of L. In this paper various convergence results are obtained for the corresponding Bergman kernels. The convergence is studied in the large k limit and is expressed in terms of the equilibrium metric associated to the fixed metric, as well as in terms of the Monge-Ampere measure of the fixed metric itself on a certain support set. It is also shown that the equilibrium metric has Lipschitz continuous first derivatives. These results can be seen as generalizations of well-known results concerning the case when the curvature of the fixed metric is positive (the corresponding equilibrium metric is then simply the fixed metric itself). | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/0704.1640 | |
| dc.identifier | http://arxiv.org/abs/0704.1640 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127284 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.title | Bergman kernels and equilibrium measures for ample line bundles | |
| dc.type | text |