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Convergence of Berg...
Convergence of Bergman measures of high powers of a line bundle
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- Berman, Robert, 1976 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology
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- Witt Nyström, David, 1980 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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(creator_code:org_t)
- 2008
- English.
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Abstract
Subject headings
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- Let L be a holomorphic line bundle on a compact complex manifold X of dimension n, and let exp(-\phi) be a continuous metric on L. Fixing a measure dμ on X gives a sequence of Hilbert spaces consisting of holomorphic sections of tensor powers of L. We prove that the corresponding sequence of scaled Bergman measures converges, in the high tensor power limit, to the equilibrium measure of the pair (K,\phi), where K is the support of dμ, as long as dμ is stably Bernstein-Markov with respect to (K,\phi). Here the Bergman measure denotes dμ times the restriction to the diagonal of the pointwise norm of the corresponding orthogonal projection operator. In particular, an extension to higher dimensions is obtained of results concerning random matrices and classical orthogonal polynomials.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- complex geometry
- pluripotential theory
- line bundles
- bergman kernel
- bergman measure
- equilibrium measure
- equilibrium measure
Publication and Content Type
- vet (subject category)
- ovr (subject category)
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