Integral representations and holomorphic extension on toric varieties.

摘要

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.