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Bergman kernels and equilibrium measures for line bundles over projective manifolds

Robert Berman (Institutionen för matematiska vetenskaper, matematik)
American Journal of Mathematics (0002-9327). Vol. 131 (2009), 5, p. 1485-1524.
[Artikel, refereegranskad vetenskaplig]

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.

Denna post skapades 2010-02-19. Senast ändrad 2016-08-16.
CPL Pubid: 113192


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Institutionen för matematiska vetenskaper, matematik (2005-2016)


Matematisk analys

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