Combinatorics of rank jumps in simplicial hypergeometric systems
| dc.creator | Matusevich, Laura Felicia | |
| dc.creator | Miller, Ezra | |
| dc.date | 2004-02-05 | |
| dc.date.accessioned | 2026-07-07T05:05:09Z | |
| dc.date.available | 2026-07-07T05:05:09Z | |
| dc.description | Let A be an integer (d x n) matrix, and assume that the convex hull conv(A) of its columns is a simplex of dimension d-1. Write \NA for the semigroup generated by the columns of A. It was proved by M. Saito [math.AG/0012257] that the semigroup ring \CC[\NA] over the complex numbers \CC is Cohen-Macaulay if and only if the rank of the GKZ hypergeometric system H_A(beta) equals the normalized volume of conv(A) for all complex parameters beta in \CC^d. Our refinement here shows, in this simplicial case, that H_A(beta) has rank strictly larger than the volume of conv(A) if and only if beta lies in the Zariski closure in \CC^d of all \ZZ^d-graded degrees where the local cohomology H^i_m(\CC[\NA]) at the maximal ideal m is nonzero for some i < d. | |
| dc.description | 6 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0402071 | |
| dc.identifier | http://arxiv.org/abs/math/0402071 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70068 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 33C70 (Primary) 14M25, 13N10, 13D45, 52B20, 13C14, 16S36, 20M25 (Secondary) | |
| dc.title | Combinatorics of rank jumps in simplicial hypergeometric systems | |
| dc.type | text |