Local complex singularity exponents for isolated singularities
Name
55635790-MIT.pdf
Description
Full printable version
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2.21 MB
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Checksum (MD5)
329a3bc849723e88ad9b9daa1bd07aa2
Author(s)
Hou, Zuoliang, 1977-
Advisor(s)
Gang Tian.
Date Issued
2004
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, I studied the stability of local complex'singularity exponents (lcse) for holomorphic functions whose zero sets have only isolated singularities. For a given holomorphic function f defined on a neighborhood of the origin in C[to the power of]n, the lcse c[sub]0(f) is defined as the supremum of all positive real number [lambda] for which 1/[magnitude of]f[to the power of][2 lambda] is integrable on some neighborhood of the origin. It has been conjectured that c[sub]0(f) should not decrease if f is deformed small enough. Using J. Mather and S.S.T. Yau's result on the classification of isolated hypersurface singularities, together with a well known result on the stability of c[sub]0(f) when f is deformed in a finite dimension base space, I proved that if the zero set of f has only isolated singularity at the origin, then c[sub]0(g) >[or equal to][sub]0(f) for g close enough to f with respect to the C⁰ norm over a neighborhood of the origin, thus gave a partial solution to the conjecture. Using the stability results, I also computed the holomorphic invariant α(M) for some special Fano manifold M.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (p. 59-61).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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