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Abstract:

We introduce a notion of balanced configurations of vectors. This is motivated by the study of rational A-hypergeometric functions in the sense of Gelfand, Kapranov and Zelevinsky. We classify balanced configurations of seven plane vectors up to GL(2, ℝ)-equivalence and deduce that the only gkz-rational toric four-folds in ℙ6 are those varieties associated with an essential Cayley configuration. We show that in this case, all rational A-hypergeometric functions may be described in terms of toric residues. This follows from studying a suitable hyperplane arrangement.

Registro:

Documento: Artículo
Título:Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6
Autor:Cattani, E.; Dickenstein, A.
Filiación:Department of Mathematics, University of Massachusetts, Amherst, MA 01003, United States
Departamento de Matematica, FCEyN, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Palabras clave:A-hypergeometric functions; Balanced configurations; Cayley configurations; Toric residues; Combinatorial mathematics; Function evaluation; Matrix algebra; Nonlinear systems; Partial differential equations; Set theory; A-hypergeometric functions; Balanced configurations; Cayley configuration; Toric residues; Vectors
Año:2004
Volumen:19
Número:1
Página de inicio:47
Página de fin:65
DOI: http://dx.doi.org/10.1023/B:JACO.0000022566.81227.03
Título revista:Journal of Algebraic Combinatorics
Título revista abreviado:J Algebraic Combinatorics
ISSN:09259899
CODEN:JAOME
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09259899_v19_n1_p47_Cattani

Referencias:

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Citas:

---------- APA ----------
Cattani, E. & Dickenstein, A. (2004) . Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6. Journal of Algebraic Combinatorics, 19(1), 47-65.
http://dx.doi.org/10.1023/B:JACO.0000022566.81227.03
---------- CHICAGO ----------
Cattani, E., Dickenstein, A. "Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6" . Journal of Algebraic Combinatorics 19, no. 1 (2004) : 47-65.
http://dx.doi.org/10.1023/B:JACO.0000022566.81227.03
---------- MLA ----------
Cattani, E., Dickenstein, A. "Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6" . Journal of Algebraic Combinatorics, vol. 19, no. 1, 2004, pp. 47-65.
http://dx.doi.org/10.1023/B:JACO.0000022566.81227.03
---------- VANCOUVER ----------
Cattani, E., Dickenstein, A. Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6. J Algebraic Combinatorics. 2004;19(1):47-65.
http://dx.doi.org/10.1023/B:JACO.0000022566.81227.03