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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 \(X\).

MSC:

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