English

On the first order asymptotics of partial Bergman kernels

Complex Variables 2018-04-03 v2 Differential Geometry

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.

Keywords

Cite

@article{arxiv.1601.00241,
  title  = {On the first order asymptotics of partial Bergman kernels},
  author = {Dan Coman and George Marinescu},
  journal= {arXiv preprint arXiv:1601.00241},
  year   = {2018}
}

Comments

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

R2 v1 2026-06-22T12:21:48.895Z