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Averaging of the Cauchy kernels and integral realization of the local residue. (English) Zbl 1186.14053
It is known that Bochner-Martinelli integral formula can be obtained by averaging of the Cauchy formula on some positive measures. In this paper similar formulas for a family of kernels of integral representation associated with toric variety are obtained. These formulas was studied by the first author in some of his previous papers. Here the mentioned kernels generalize the considered integral forms. Applications are given for integral realization of the local residue in algebraic geometry. The paper is interesting for a broad circle of specialists.

14M25 Toric varieties, Newton polyhedra, Okounkov bodies
32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels)
32A27 Residues for several complex variables
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