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dc.contributor.advisorGang Tian.en_US
dc.contributor.authorHou, Zuoliang, 1977-en_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.date.accessioned2005-09-26T19:43:06Z
dc.date.available2005-09-26T19:43:06Z
dc.date.copyright2004en_US
dc.date.issued2004en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/28312
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.en_US
dc.descriptionIncludes bibliographical references (p. 59-61).en_US
dc.description.abstractIn 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.en_US
dc.description.statementofresponsibilityby Zuoliang Hou.en_US
dc.format.extent61 p.en_US
dc.format.extent2310260 bytes
dc.format.extent2315816 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.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.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582
dc.subjectMathematics.en_US
dc.titleLocal complex singularity exponents for isolated singularitiesen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.identifier.oclc55635790en_US


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