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arXiv · 1505.08050

Equidistribution speed for Fekete points associated with an ample line bundle

Tien-Cuong Dinh·Xiaonan Ma·Viet-Anh Nguyen
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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 at most p. A recent theorem by Berman, Boucksom and Witt Nystrom implies that Fekete configurations for K are asymptotically equidistributed with respect to a canonical equilibrium measure, as p tends to infinite. 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.

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Tien-Cuong Dinh, Xiaonan Ma, Viet-Anh Nguyen. 2015-05-29. Equidistribution speed for Fekete points associated with an ample line bundle. https://arxiv.org/abs/1505.08050

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