Bergman kernel and stability of holomorphic vector bundles with sections
Name
54790435-MIT.pdf
Description
Full printable version
Size
3.97 MB
Format
Adobe PDF
Checksum (MD5)
e1a7641e25626f77524d4c5291c591d1
Author(s)
Wang, Lijing, 1975-
Advisor(s)
Gang Tian.
Date Issued
2003
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.
Includes bibliographical references (p. 83-85).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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