Integral representations and holomorphic extension on toric varieties |
Posted on:2006-07-22 | Degree:Ph.D | Type:Thesis |
University:University of Missouri - Rolla | Candidate:Kytmanov, Alexey Alexandrovich | Full Text:PDF |
GTID:2450390008971465 | Subject:Mathematics |
Abstract/Summary: | |
This thesis deals with integral representations for holomorphic functions and holomorphic extensions in several complex variables. These two problems are considered on toric varieties.;We will construct volume forms o0([zeta]) on toric varieties X (analogues of Fubini-Studi form) and etalon forms o(zeta) in Cd Z(Sigma), where Z(Sigma) is a union of some coordinate subspaces in Cd . This will allow us to construct a class of integral representations in d-circular polyhedra with etalon kernels o(zeta).;Another object of study in the dissertation is a problem of holomorphic extension of CR-functions on toric varieties. We will consider the compact and noncompact cases and investigate some restrictions on varieties under which such an extension becomes possible. |
Keywords/Search Tags: | Integral representations, Extension, Holomorphic, Varieties |
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