Stability of the Bergman kernel on a tower of coverings

Details Stability of the Bergman kernel on a tower of coverings Stability of the Bergman kernel on a tower of coverings

2012-02-20

arxiv.org/abs/1202.4371v1

Mathematics

Complex Variables

22 pages

Scientific paper

We obtain several results about stability of the Bergman kernel on a tower of coverings on complex manifolds. An effective version of Rhodes' result is given for a tower of coverings on a compact Riemann surface of genus greater than or equal to 2. Stability of the Bergman kernel is established for towers of coverings on hyperbolic Riemann surfaces and on complete Kaehler manifolds satisfying certain potential conditions. As a consequence, stability of the Bergman kernel is established for any tower of coverings of Riemann surfaces when the top manifold is simply-connected.

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