Equidistribution speed for Fekete points associated with an ample line bundle

Abstract

Let K be the closure of a bounded open set with smooth boundary in C n . A Fekete configuration of order p for K is a finite subset of K maximizing the Vandermonde determinant associated with polynomials of degree p. A recent theorem by Berman, Boucksom and Witt Nystrimplies that Fekete configurations for K are asymptotically equidistributed with respect to a canonical equilibrium measure, as p!1. We give here an explicit estimate for the speed of convergence. The result also holds in a general setting of Fekete points associated with an ample line bundle over a projective manifold. Our approach requires a new estimate on Bergman kernels for line bundles and quantitative results in pluripotential theory which are of independent interest. Classification AMS 2010: 32U15 (32L05).