We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their equidistribution is a known result. The novelty of our approach is that we relate them to the problem of sampling and interpolation on line bundles, which allows us to estimate the equidistribution of the Fekete points quantitatively. In particular we estimate the Kantorovich-Wasserstein distance of the Fekete points to the limiting measure. The sampling and interpolation arrays on line bundles are a subject of independent interest, and we provide necessary density conditions through the classical approach of Landau, that in this context measures the local dimension of the space of sections of the line bundle. We obtain a complete geometric characterization of sampling and interpolation arrays in the case of compact manifolds of dimension one, and we prove that there are no arrays of both sampling and interpolation in the more general setting of semipositive line bundles.
Bibliographical noteFunding Information:
Part of this work was done while Nir Lev was staying at the Centre de Recerca Matemàtica (CRM) in Barcelona, and he would like to express his gratitude to the institute for hospitality and support during his stay. Nir Lev is partially supported by the Israel Science Foundation grant No. 225/13 and Joaquim Ortega-Cerdà is supported by the project MTM2014-51834-P and the CIRIT grant 2014SGR-289.
© European Mathematical Society 2016.
- Beurling-Landau density
- Fekete points
- Holomorphic line bundles