On the first order asymptotics of partial Bergman kernels

Abstract

We show that under very general assumptions the partial Bergman kernel function of sections vanishing along an analytic hypersurface has exponential decay in a neighborhood of the vanishing locus. Considering an ample line bundle, we obtain a uniform estimate of the Bergman kernel function associated to a singular metric along the hypersurface. Finally, we study the asymptotics of the partial Bergman kernel function on a given compact set and near the vanishing locus.

16 pages; v.2 is a final update to agree with the published paper

References in corpus (2)

• Equidistribution for sequences of line bundles on normal Kaehler spaces
• Interface asymptotics of partial Bergman kernels on $S^1$-symmetric Kaehler manifolds

Cited by in corpus (3)

• Bergman kernels on punctured Riemann surfaces
• The asymptotics of the optimal holomorphic extensions of holomorphic jets along submanifolds
• Off-diagonal estimates of partial Bergman kernels on $S^1$-symmetric Kähler manifolds