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Mathematical Research Letters
Volume 27 (2020)
Number 3
Quantitative upper bounds for Bergman kernels associated to smooth Kähler potentials
Pages: 743 – 787
DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n3.a7
Authors
Abstract
We prove upper bounds for the Bergman kernels associated to tensor powers of a smooth positive line bundle in terms of the rate of growth of the Taylor coefficients of the Kähler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevrey potentials.
Received 1 August 2018
Accepted 23 September 2018
Published 20 August 2020