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Bergman kernels and equilibrium measures for line bundles over projective manifolds

Författare och institution:
Robert Berman (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
American Journal of Mathematics, 131 ( 5 ) s. 1485-1524
Artikel, refereegranskad vetenskaplig
Sammanfattning (abstract):
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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
Matematik ->
Matematisk analys
Postens nummer:
Posten skapad:
2010-02-19 12:58
Posten ändrad:
2016-08-16 10:20

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