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.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1601.00241
 Bibcode:
 2016arXiv160100241C
 Keywords:

 Mathematics  Complex Variables;
 Mathematics  Differential Geometry
 EPrint:
 16 pages