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Title:Contributions to the Model Theory of Fields and Compact Complex Spaces
Author(s):Moosa, Rahim Nazim
Doctoral Committee Chair(s):Pillay, Anand
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
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.
Issue Date:2001
Description:94 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.
Other Identifier(s):(MiAaPQ)AAI3023146
Date Available in IDEALS:2015-09-28
Date Deposited:2001

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