Upper bounds for Bergman kernels associated to positive line bundles\n with smooth Hermitian metrics

2013/07/31 by Michael Christ, Christ, Michael · 2 citations
Mathematics · #32W05 #58J37 #Advanced Algebra and Geometry #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1308.0062

openalex publication_date 2013/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Off-diagonal upper bounds are established away from the diagonal for the\nBergman kernels associated to high powers of holomorphic line bundles over\ncompact complex manifolds, asymptotically as the power tends to infinity. The\nline bundle is assumed to be equipped with a Hermitian metric with positive\ncurvature form, which is infinitely differentiable but not necessarily real\nanalytic. The bounds obtained are the best possible for this class of metrics.\n

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• Off-diagonal estimates of the Bergman kernel associated to Siegel varieties

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