Algorithm for construction of volume forms on toric varieties starting from a convex integer polytope

Abstract

This paper presents a method and a corresponding algorithm for constructing volume forms (and related forms that act as kernels of integral representations) on toric varieties from a convex integer polytope. The algorithm is implemented in the Maple computer algebra system. The constructed volume forms are similar to the volume forms of the Fubini---Study metric on a complex projective space and can be used for constructing integral representations of holomorphic functions in polycircular regions of a multidimensional complex space.