Bivariate rational hypergeometric functions and residues

E. CATTANI, A. DICKENSTEIN, F. RODRIGUEZ VILLEGAS

Bloomington, Indiana, EEUU

Congreso; Session on D-modules, Regional AMS Meeting; 2008

American Mathematical Society

We show that for any Cayley configuration A of codimension two, a sufficiently high derivative of any rational function solution of the associated A-hypergeometric system is a toric residue. This follows from the fact that the dimension of the space of rational A-hypergeometric functions with homogeneities in the Euler-Jacobi cone of A equals 1 and is spanned by an explicit toric residue we read from the configuration and the homogeneity. This gives a geometric interpretation of monodromy invariant A-hypergeometric functions for codimension two configurations.