Algebraic solutions of GKZ-hypergeometric systems and toric residues.

A DICKENSTEIN, E. CATTANI Y F. MARTÍNEZ

Guanajuato

Congreso; Mathematical Congress of the Americas 2013; 2013

CIMAT

GKZ-hypergeometric systems of partial differential equations (named after Gelfand, Kapranov and Zelevinsky) have natural geometric solutions, with singularities on the associated (full) discriminant. We describe GKZ-hypergeometric algebraic Laurent series associated with Cayley congurations of n lattice congurations in n space. We show that these algebraic series are generated by certain combinatorially dened sums of point residues, whose computation can be interpreted in terms of a toric degeneration.