Geodesic
Planar configurations of lattice vectors and GKZ-rational toric fourfolds in $\Bbb P^6$
Journal of Algebraic Combinatorics, Tome 19 (2004) no. 1, pp. 47-65.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $G$L(2, $Ropf$)-equivalence and deduce that the only gkz-rational toric four-folds in $Popf ^{6}$ 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.
Classification : Primary, 33C70,, Secondary, 05B35,, 32A27
Keywords: $A$-hypergeometric functions, toric residues, balanced configurations, Cayley configurations 
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     title = {Planar configurations of lattice vectors and {GKZ-rational} toric fourfolds in $\Bbb P^6$},
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Cattani, Eduardo; Dickenstein, Alicia. Planar configurations of lattice vectors and GKZ-rational toric fourfolds in $\Bbb P^6$. Journal of Algebraic Combinatorics, Tome 19 (2004) no. 1, pp. 47-65. http://geodesic.mathdoc.fr/item/JAC_2004__19_1_a2/