Toric Varieties in Several Complex Variables

The present book deals with integral representations for holomorphic functions of several complex variables and holomorphic extensions in several complex variables. We construct volume forms on toric varieties (analogues of the Fubini-Studi form) and etalon forms in multidimensional complex space with singular set a union of some coordinate subspaces (analogues of the Bochner-Martinelli form). This will allow us to construct a class of integral representations in d-circular polyhedra with etalon kernels. Another object of study in the work 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.