Bergman kernels and equilibrium measures for line bundles over projective manifolds
| dc.creator | Berman, Robert | |
| dc.date | 2007-10-24 | |
| dc.date | 2007-12-25 | |
| dc.date.accessioned | 2026-07-07T08:50:58Z | |
| dc.date.available | 2026-07-07T08:50:58Z | |
| dc.description | Let L be a holomorphic line bundle over a compact complex projective Hermitian manifold X. Any fixed smooth hermitian metric h 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 (i.e. orthogonal projection kernels). The convergence is studied in the large k limit and is expressed in terms of the equilibrium metric h_e associated to h, as well as in terms of the Monge-Ampere measure of h on a certain support set. It is also shown that the equilibrium metric h_e is in the class C^{1,1} on the complement of the augmented base locus of L. For L ample these results give generalizations of well-known results concerning the case when the curvature of h is globally positive (then h_e=h). In general, the results can be seen as local metrized versions of Fujita's approximation theorem for the volume of L. | |
| dc.description | 35 pages. This paper supersedes "Bergman kernels and equilibrium measures for ample line bundles" (apart from section 4 that will be superseded by a sequal to this paper) v2: two pictures added. Fixed some confusing typos in the proof of lemma 4.4 | |
| dc.identifier | https://arxiv.org/abs/0710.4375 | |
| dc.identifier | http://arxiv.org/abs/0710.4375 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144779 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.title | Bergman kernels and equilibrium measures for line bundles over projective manifolds | |
| dc.type | text |