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Quantitative upper bounds for Bergman kernels associated to smooth Kähler potentials (1807.00204v1)
Published 30 Jun 2018 in math.CV, math.AP, and math.DG
Abstract: We give 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 K\"ahler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevrey potentials.