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Fekete points and convergence towards equilibrium measures on complex manifolds

Magazine article
Authors Robert Berman
Sebastien Boucksom
David Witt Nyström
Published in Acta Mathematica
Volume 207
Issue 1
Pages 1-27
ISSN 1871-2509
Publication year 2011
Published at Department of Mathematical Sciences
Department of Mathematical Sciences, Mathematics
Pages 1-27
Language en
Links arxiv.org/abs/0907.2820
dx.doi.org/10.1007/s11511-011-0067-...
Subject categories Mathematics

Abstract

Building on the first two authors' previous results, we prove a general criterion for convergence of (possibly singular) Bergman measures towards equilibrium measures on complex manifolds. The criterion may be formulated in terms of growth properties of balls of holomorphic sections, or equivalently as an asymptotic minimization of generalized Donaldson L-functionals. Our result yields in particular the proof of a well-known conjecture in pluripotential theory concerning the equidistribution of Fekete points, and it also gives the convergence of Bergman measures towards equilibrium for Bernstein-Markov measures. Applications to interpolation of holomorphic sections are also discussed.

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