Equidistribution estimates for Fekete points on complex manifolds
Lev, Nir
Ortega Cerdà, Joaquim
Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica

Imprint: Centre de Recerca Matemàtica 2012
Description: 38 p.
Abstract: 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 its 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.
Rights: L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: Creative Commons
Language: Anglès.
Series: Centre de Recerca Matemàtica: Prepublicacions del Centre de Recerca Matemàtica
Series: Prepublicacions del Centre de Recerca Matemàtica ; 1122
Document: article ; submittedVersion
Subject: Varietats complexes ; Densitat funcional ; Punts fixos,Teoria dels ; Feixos de fibres (Matemàtica)

Adreça alternativa: https://hdl.handle.net/2072/206096


38 p, 355.2 KB

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Research literature > Preprints

 Record created 2018-10-23, last modified 2019-07-16



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