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


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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.

About the authors

A. A. Kytmanov

Siberian Federal University

Author for correspondence.
Email: aakytm@gmail.com
Russian Federation, pr. Svobodnyi 79, Krasnoyarsk, 660041

A. V. Shchuplev

Siberian Federal University

Email: aakytm@gmail.com
Russian Federation, pr. Svobodnyi 79, Krasnoyarsk, 660041

T. V. Zykova

Siberian Federal University

Email: aakytm@gmail.com
Russian Federation, pr. Svobodnyi 79, Krasnoyarsk, 660041

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