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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.

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Correspondence to A. A. Kytmanov.

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Original Russian Text © A.A. Kytmanov, A.V. Shchuplev, T.V. Zykova, 2016, published in Programmirovanie, 2016, Vol. 42, No. 2.

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Kytmanov, A.A., Shchuplev, A.V. & Zykova, T.V. Algorithm for construction of volume forms on toric varieties starting from a convex integer polytope. Program Comput Soft 42, 99–106 (2016). https://doi.org/10.1134/S0361768816020055

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  • DOI: https://doi.org/10.1134/S0361768816020055

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