Kytmanov, A. A. An analog of the Fubini-Studi form for two-dimensional toric varieties. (Russian, English) Zbl 1081.32004 Sib. Mat. Zh. 44, No. 2, 358-371 (2003); translation in Sib. Math. J. 44, No. 2, 286-297 (2003). Summary: For two-dimensional toric varieties \(X\), an analog of the Fubini-Studi form \(\omega_0\) is constructed together with the canonical form \(\omega\) that is the kernel of an integral representation for holomorphic functions in \(d\)-circular domains in \(\mathbb C^d\) connected with two-dimensional toric varieties \(X\). This kernel is shown to be a closed differential form in \(\mathbb C^d\) defining the associated positive form \(\omega_0\) on \(X\). Cited in 8 Documents MSC: 32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) 14M25 Toric varieties, Newton polyhedra, Okounkov bodies Keywords:Bochner-Martinelli integral representation; projective space; volume form; fan PDFBibTeX XMLCite \textit{A. A. Kytmanov}, Sib. Mat. Zh. 44, No. 2, 358--371 (2003; Zbl 1081.32004); translation in Sib. Math. J. 44, No. 2, 286--297 (2003) Full Text: EuDML EMIS