Balanced Configurations of Lattice Vectors and GKZ-rational Toric Fourfolds in P^6
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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 complex projective space P^6 are those varieties associated with an essential Cayley configuration. In this case, we study a suitable hyperplane arrangement and show that all rational A-hypergeometric functions may be described in terms of toric residues.
Revised version to appear in the Journal of Algebraic Combinatorics. The new proof of Theorem 2.14 is inspired by the proof of N. Ressayre in math.RA/0206234 of a conjecture we raised in the previous version of this article
Revised version to appear in the Journal of Algebraic Combinatorics. The new proof of Theorem 2.14 is inspired by the proof of N. Ressayre in math.RA/0206234 of a conjecture we raised in the previous version of this article