Bergman kernel and stability of holomorphic vector bundles with sections

In this thesis, we introduce a notion of asymptotic stability for a holomorphic vector bundle with a global holomorphic section on a projective manifold. We prove that the special metric on the bundle studied by Bradlow is the limit of a sequence of balanced metrics that are induced from the asymptotic stability. Conversely, assuming the convergence of a sequence of balanced metrics, we show that the sequence converge to a special metric in the sense of Bradlow. The proof uses the asymptotic expansion of the Bergman kernel for general holomorphic vector bundle and machineries about moment maps involving two group actions developed by Donaldson.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2003

Author dc:creator

• Wang, Lijing, 1975-

Advisor dc:contributor.advisor

• Gang Tian.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/29983

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/29983