On the $b$-functions of hypergeometric systems

Abstract

For any integer $d\times (n+1)$ matrix $A$ and parameter $β\in\CC^d$ let $M_A(\beta )$ be the associated $A$-hypergeometric (or GKZ) system in the variables $x_0,\dots ,x_n$. We describe bounds for the (roots of the) $b$-functions of both $M_A(\beta )$ and its Fourier transform along the hyperplanes $(x_j=0)$. We also give an estimate for the $b$-function for restricting $M_A(\beta )$ to a generic point.

14 pages, several figures. Typos corrected

References in corpus (5)

• Irregularity of hypergeometric systems via slopes along coordinate subspaces
• Hypergeometric D-modules and twisted Gauss-Manin systems
• Laurent Polynomials, GKZ-hypergeometric Systems and Mixed Hodge Modules
• Hypergeometric Hodge modules
• Cohen-Macaulayness and computation of Newton graded toric rings