Fekete points and convergence towards equilibrium measures on complex manifolds

• 成果类型: Article
• 署名作者: Berman, Robert; Boucksom, Sebastien; Nystrom, David Witt
• 署名单位: Chalmers University of Technology; University of Gothenburg; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-011-0067-x
• 发表日期: 2011
• 页码: 1-27
• 关键词: bergman kernels; LINE BUNDLES; interpolation; POLYNOMIALS; CURVES; nodes

摘要

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.