Singularities and holonomicity of binomial D-modules

TL;DR

This paper investigates binomial D-modules, extending A-hypergeometric systems, by explicitly determining their singular loci and providing three characterizations of their holonomicity, including criteria based on singular loci and L-holonomicity.

Contribution

It offers explicit descriptions of singular loci and three new characterizations of holonomicity for binomial D-modules, enhancing understanding of their structure.

Findings

Holonomic binomial D-modules have proper singular loci.

Holonomicity is equivalent to L-holonomicity for these systems.

Detailed information about the L-characteristic variety of non-holonomic modules.

Abstract

We study binomial D-modules, which generalize A-hypergeometric systems. We determine explicitly their singular loci and provide three characterizations of their holonomicity. The first of these states that a binomial D-module is holonomic if and only if its corresponding singular locus is proper. The second characterization is an equivalence of holonomicity and L-holonomicity for these systems. The third refines the second by giving more detailed information about the L-characteristic variety of a non-holonomic binomial D-module.