Fekete points and convergence towards equilibrium measures on complex manifolds |
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Authors: | Robert Berman Sébastien Boucksom David Witt Nyström |
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Affiliation: | 1.Department of Mathematics,Chalmers University of Technology and University of G?teborg,G?teborg,Sweden;2.Institut de Mathématiques,CNRS-Université Pierre et Marie Curie,Paris Cedex 05,France |
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Abstract: | Building on [BB1] we prove a general criterion for convergence of (possibly singular) Bergman measures towards pluripotential-theoretic equilibrium measures on complex manifolds. The criterion may be formulated in terms of the growth properties of the unit-balls of certain norms on holomorphic sections, or equivalently as an asymptotic minimization property for generalized Donaldson L-functionals. Our result settles in particular a well-known conjecture in pluripotential theory concerning the equidistribution of Fekete points and it gives the convergence of Bergman measures towards the equilibrium measure for Bernstein-Markov measures. Applications to interpolation of holomorphic sections are also discussed. |
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