Abstract/Details

The geometry of the Deligne-Hodge decomposition


1999 1999

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Abstract (summary)

In this thesis we explore variations of mixed Hodge structures, both locally and asymptotically. First, making use of certain distinguished gradings of the Hodge and weight filtrations, I compute the curvature of appropriate classifying spaces and Hodge bundles relative to a natural “mixed” Hodge metric. Second, I obtain appropriate generalizations of the Nilpotent Orbit Theorem for admissible variations, norm estimates, a version of the invariant cycle Theorem, and extend an equivalence of categories theorem of Deligne. Third, I demonstrate the existence of canonical Higgs fields associated to such variations and discuss their relations with a partial interpretation of Mirror Symmetry due to Deligne.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences, Decompositions, Deligne-Hodge, Geometry, Higgs
Title
The geometry of the Deligne-Hodge decomposition
Author
Pearlstein, Gregory James
Number of pages
107
Publication year
1999
Degree date
1999
School code
0118
Source
DAI-B 60/05, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780599329102, 0599329106
Advisor
Kaplan, Aroldo
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9932337
ProQuest document ID
304536353
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304536353
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