Planar Configurations of Lattice Vectors and GKZ-rational Toric Fourfolds in P^6

E.CATTANI; A. DICKENSTEIN

JOURNAL OF ALGEBRAIC COMBINATORICS

Año: 2004 vol. 19 p. 47 - 65

0925-9899

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.