Fekete points and convergence towards equilibrium measures on complex manifolds
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.
Cite
@article{arxiv.0907.2820,
title = {Fekete points and convergence towards equilibrium measures on complex manifolds},
author = {Robert J. Berman and Sebastien Boucksom and David Witt Nystrom},
journal= {arXiv preprint arXiv:0907.2820},
year = {2009}
}
Comments
26 pages, supersedes our previous papers arXiv:0805.2846 and arXiv:0807.0035