Combinatorics of rank jumps in simplicial hypergeometric systems


Journal Article

Let A be an integer d × n matrix, and assume that the convex hull conv(A) of its columns is a simplex of dimension d - 1 not containing the origin. It is known that the semigroup ring ℂ[Ndbl;A] is Cohen-Macaulay if and only if the rank of the GKZ hypergeometric system H A(β) equals the normalized volume of conv(A) for all complex parameters β ε ℂ d (Saito, 2002). Our refinement here shows that H A(β) has rank strictly larger than the volume of conv(A) if and only if β lies in the Zariski closure (in ℂ d) of all Zdbl; d-graded degrees where the local cohomology ⊕ i

Full Text

Duke Authors

Cited Authors

  • Matusevich, LF; Miller, E

Published Date

  • May 1, 2006

Published In

Volume / Issue

  • 134 / 5

Start / End Page

  • 1375 - 1381

International Standard Serial Number (ISSN)

  • 0002-9939

Digital Object Identifier (DOI)

  • 10.1090/S0002-9939-05-08245-6

Citation Source

  • Scopus