Quantitative upper bounds for Bergman kernels associated to smooth Kähler potentials (Q1996246)

The authors 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, they also obtain improved off-diagonal rates of decay for the classes of analytic, quasi-analytic, and, more generally, Gevrey potentials.