Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve
M.C. Fernandez-Fernandez, F.J. Castro-Jimenez (University of, Seville, Spain)
TL;DR
This paper investigates the Gevrey series solutions and irregularity of the GKZ hypergeometric system linked to an affine monomial curve, utilizing D-module theory to analyze singular points.
Contribution
It provides a detailed description of Gevrey solutions and the irregularity complex for these systems, reducing the problem to a two-dimensional case using D-module techniques.
Findings
Explicit characterization of Gevrey solutions at singular points
Description of the irregularity complex with respect to singular support
Reduction of the problem to a two-dimensional case
Abstract
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine monomial curve. We also describe the irregularity complex of such a system with respect to its singular support. We use restriction and some results in D-module theory to reduce our study to the two dimensional case.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory