Singularities and holonomicity of binomial D-modules

Christine Berkesch Zamaere; Laura Felicia Matusevich; Uli Walther

doi:10.1016/j.jalgebra.2015.04.030

Singularities and holonomicity of binomial D-modules

Christine Berkesch Zamaere, Laura Felicia Matusevich, Uli Walther

School of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 is an equivalence of holonomicity and L-holonomicity for these systems. The second refines the first by giving more detailed information about the L-characteristic variety of a non-holonomic binomial D-module. The final characterization states that a binomial D-module is holonomic if and only if its corresponding singular locus is proper.

Original language	English (US)
Pages (from-to)	360-372
Number of pages	13
Journal	Journal of Algebra
Volume	439
DOIs	https://doi.org/10.1016/j.jalgebra.2015.04.030
State	Published - Oct 1 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

A-discriminant
Binomial D-module
Holonomic
Hypergeometric
Primary
Secondary
Singularity

Publisher link

10.1016/j.jalgebra.2015.04.030

Find It

Find It at U of M Libraries

Cite this

@article{14ff29092d5046fabbbcbc9c7bf22e5b,

title = "Singularities and holonomicity of binomial D-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 is an equivalence of holonomicity and L-holonomicity for these systems. The second refines the first by giving more detailed information about the L-characteristic variety of a non-holonomic binomial D-module. The final characterization states that a binomial D-module is holonomic if and only if its corresponding singular locus is proper.",

keywords = "A-discriminant, Binomial D-module, Holonomic, Hypergeometric, Primary, Secondary, Singularity",

author = "{Berkesch Zamaere}, Christine and Matusevich, {Laura Felicia} and Uli Walther",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2015",

month = oct,

day = "1",

doi = "10.1016/j.jalgebra.2015.04.030",

language = "English (US)",

volume = "439",

pages = "360--372",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Singularities and holonomicity of binomial D-modules

AU - Berkesch Zamaere, Christine

AU - Matusevich, Laura Felicia

AU - Walther, Uli

PY - 2015/10/1

Y1 - 2015/10/1

N2 - 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 is an equivalence of holonomicity and L-holonomicity for these systems. The second refines the first by giving more detailed information about the L-characteristic variety of a non-holonomic binomial D-module. The final characterization states that a binomial D-module is holonomic if and only if its corresponding singular locus is proper.

AB - 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 is an equivalence of holonomicity and L-holonomicity for these systems. The second refines the first by giving more detailed information about the L-characteristic variety of a non-holonomic binomial D-module. The final characterization states that a binomial D-module is holonomic if and only if its corresponding singular locus is proper.

KW - A-discriminant

KW - Binomial D-module

KW - Holonomic

KW - Hypergeometric

KW - Primary

KW - Secondary

KW - Singularity

UR - http://www.scopus.com/inward/record.url?scp=84930958794&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84930958794&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2015.04.030

DO - 10.1016/j.jalgebra.2015.04.030

M3 - Article

AN - SCOPUS:84930958794

SN - 0021-8693

VL - 439

SP - 360

EP - 372

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Singularities and holonomicity of binomial D-modules

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this