University of Illinois Urbana-Champaign

Contributions to the Model Theory of Fields and Compact Complex Spaces

Moosa, Rahim Nazim

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https://hdl.handle.net/2142/86786

Description

Title
Contributions to the Model Theory of Fields and Compact Complex Spaces
Author(s)
Moosa, Rahim Nazim
Issue Date
2001
Doctoral Committee Chair(s)
Pillay, Anand
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
"While the methods of geometric stability theory have traditionally been applied to algebraic rather than analytic geometry, it has been observed that these techniques are also meaningful when applied to compact complex analytic spaces. One obstacle is that these structures are not saturated in the natural language of their analytic sets. The notion of a Zariski closed set in an elementary extension of a compact complex space, as well as the associated complex dimension, are discussed. It is shown that a one-dimensional Zariski closed set in an elementary extension of a compact complex space is essentially algebraic. This provides a kind of nonstandard version of the Riemann Existence Theorem. The notion of a ""saturated"" compact complex analytic space, where it is not necessary to pass to elementary extensions, is also introduced. A characterisation of such spaces in terms of the Douady spaces of their cartesian powers, as well as an application to relative algebraic reductions, is given."
Graduation Semester
2001
Type of Resource
text
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http://hdl.handle.net/2142/86786

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