Quantitative upper bounds for Bergman kernels associated to smooth Kähler potentials

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 Kähler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevrey potentials.

arXiv comment28 pages

References in corpus (6)

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Cited by in corpus (2)

• On a property of Bergman kernels when the Kähler potential is analytic
• Asymptotic properties of Bergman kernels for potentials with Gevrey regularity