Integral Representations and Volume Forms on Hirzebruch Surfaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 2, pp. 125-132.

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We construct a class of integral representations for holomorphic functions in a polyhedron in $\mathbb C^4$, associated with Hirzebruch surfaces. The kernels of the integral representations are closed differential forms in $\mathbb C^4$ associated with volume forms on Hirzebruch surfaces.
Keywords: integral representation, toric variety.
Mots-clés : Hirzebruch surface
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Alexey A. Kytmanov. Integral Representations and Volume Forms on Hirzebruch Surfaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 2, pp. 125-132. http://geodesic.mathdoc.fr/item/JSFU_2008_1_2_a1/

[1] P. Griffiths, J. Harris, Principles of algebraic geometry, John Wiley Sons, New York et al., 1978 | MR | Zbl

[2] A. M. Kytmanov, The Bochner-Martinelli Integral and its Applications, Birkhäuser Verlag, Basel et al., 1995 | MR | Zbl

[3] B. V. Shabat, Value distribution of holomorphic mappings, Nauka, Moscow, 1982 | MR

[4] M. Audin, The Topology of Torus Actions on Symplectic Manifolds, Progress in Math., 93, Birkhäuser Verlag, Boston et al., 1991 | MR | Zbl

[5] D. A. Cox, Recent Developments in Toric geometry, Proc. Symp. Pure Math., 62, Part 2, Amer. Math. Soc., Providence, RI, 1997 | MR | Zbl

[6] D. A. Cox, “Toric Residues”, Ark. Mat., 34:1 (1996), 73–96 | DOI | MR | Zbl

[7] A. A. Kytmanov, “An analog of the Fubini–Studi form for two-dimensional toric varieties”, Sib. Mat. Zh., 44:2 (2003), 358–371 | MR | Zbl

[8] V. Guillemin, Moment Maps and Combinatorial Invariants of Hamiltonian $T^n$-spaces, Progress in Math., 122, Birkhäuser Verlag, Boston et al., 1994 | MR | Zbl