Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6

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-rati...

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Detalles Bibliográficos
Autores principales: Cattani, Eduardo H.C., Dickenstein, Alicia Marcela
Publicado: 2004
Materias:
A-hypergeometric functions
Balanced configurations
Cayley configurations
Toric residues
Combinatorial mathematics
Function evaluation
Matrix algebra
Nonlinear systems
Partial differential equations
Set theory
Cayley configuration
Vectors
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09259899_v19_n1_p47_Cattani
http://hdl.handle.net/20.500.12110/paper_09259899_v19_n1_p47_Cattani
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_09259899_v19_n1_p47_Cattani
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spelling paper:paper_09259899_v19_n1_p47_Cattani2023-06-08T15:51:32Z Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6 Cattani, Eduardo H.C. Dickenstein, Alicia Marcela 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 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. Fil:Cattani, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2004 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09259899_v19_n1_p47_Cattani http://hdl.handle.net/20.500.12110/paper_09259899_v19_n1_p47_Cattani
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 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
spellingShingle 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
Cattani, Eduardo H.C.
Dickenstein, Alicia Marcela
Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6
topic_facet 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
description 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.
author Cattani, Eduardo H.C.
Dickenstein, Alicia Marcela
author_facet Cattani, Eduardo H.C.
Dickenstein, Alicia Marcela
author_sort Cattani, Eduardo H.C.
title Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6
title_short Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6
title_full Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6
title_fullStr Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6
title_full_unstemmed Planar configurations of lattice vectors and GKZ-rational toric fourfolds in ℙ6
title_sort planar configurations of lattice vectors and gkz-rational toric fourfolds in ℙ6
publishDate 2004
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09259899_v19_n1_p47_Cattani
http://hdl.handle.net/20.500.12110/paper_09259899_v19_n1_p47_Cattani
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AT dickensteinaliciamarcela planarconfigurationsoflatticevectorsandgkzrationaltoricfourfoldsinp6
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