Binomial D-modules

A. DICKENSTEIN, L. MATUSEVICH, E. MILLER

DUKE MATHEMATICAL JOURNAL

DUKE UNIV PRESS

Año: 2010 vol. 151 p. 385 - 429

0012-7094

We study quotients of the Weyl algebra by left ideals whose generators consist of an arbitrary Z^d-graded binomial ideal I in C[partial_1, ..., partial_n] along with Euler operators definedby the grading and a parameter beta in C^d. We determine the parameters for which theseD-modules (i) are holonomic (equivalently, regular holonomic, when I is standard-graded);(ii) decompose as direct sums indexed by the primary components of I; and (iii) have holonomicrank greater than the rank for generic . In each of these three cases, the parameters inquestion are precisely those outside of a certain explicitly described affine subspace arrangementin C^d. In the special case of Horn hypergeometric D-modules, when I is a lattice basisideal, we furthermore compute the generic holonomic rank combinatorially and write downa basis of solutions in terms of associated A-hypergeometric functions. This study relies fundamentally on the explicit lattice point description of the primary components of an arbitrarybinomial ideal in characteristic zero, which we derive in our companion article [DMM08].