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Balanced Configurations Of Lattice Vectors And Gkz-Rational Toric Fourfolds In P^6, Eduardo Cattani, Alicia Dickenstein

Eduardo Cattani

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.