2008
DOI: 10.1215/00127094-2008-011
|View full text |Cite
|
Sign up to set email alerts
|

Irregularity of hypergeometric systems via slopes along coordinate subspaces

Abstract: Abstract. We study the irregularity sheaves attached to the A-hypergeometric D-module M A (β) introduced by I.M. Gel'fand et al. [GGZ87,GZK89], where A ∈ Z d×n is pointed of full rank and β ∈ C d . More precisely, we investigate the slopes of this module along coordinate subspaces.In the process we describe the associated graded ring to a positive semigroup ring for a filtration defined by an arbitrary weight vector L on torusequivariant generators. To this end we introduce the (A, L)-umbrella, a cell complex … Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2
1

Citation Types

0
96
0

Year Published

2009
2009
2022
2022

Publication Types

Select...
7
2

Relationship

1
8

Authors

Journals

citations
Cited by 55 publications
(96 citation statements)
references
References 25 publications
0
96
0
Order By: Relevance
“…When A is homogeneous, this follows from the fact that D/H A (β) is a regular holonomic D-module [Hot91], by the method of canonical series [SST00, Sections 2.5 and 2.6]. If A is not homogeneous, then D/H A (β) has irregular singularities [SW08] (these systems are also known as confluent), but if the domain of expansion is adequately chosen, one can still write A-hypergeometric functions as Nilsson series [DMM12].…”
Section: The D-module D/h a (β) Is Known As The A-hypergeometric D-momentioning
confidence: 99%
See 1 more Smart Citation
“…When A is homogeneous, this follows from the fact that D/H A (β) is a regular holonomic D-module [Hot91], by the method of canonical series [SST00, Sections 2.5 and 2.6]. If A is not homogeneous, then D/H A (β) has irregular singularities [SW08] (these systems are also known as confluent), but if the domain of expansion is adequately chosen, one can still write A-hypergeometric functions as Nilsson series [DMM12].…”
Section: The D-module D/h a (β) Is Known As The A-hypergeometric D-momentioning
confidence: 99%
“…In general, the GG systems corresponding to the hypergeometric equations studied here give rise to the solutions of those systems for generic parameters, as is stated in [GG99, The algorithm to compute canonical series solutions presented in [SST00, Section 2.6] applies to all regular holonomic left D-ideals. For an A-hypergeometric system, regular holonomicity is equivalent to the matrix A being homogeneous [Hot91,SW08], an assumption which we impose for the remainder of this section. …”
Section: The D-module D/h a (β) Is Known As The A-hypergeometric D-momentioning
confidence: 99%
“…That is the case with Examples 1-5 above for generic β. Note also that Schulze and Walther [12] described the slopes of H A (β) along coordinate subvarieties in terms of what they call (A, L)-umbrellas under the condition that the column vectors of A are contained in a proper convex cone with vertex at the origin.…”
Section: Example 1 Setmentioning
confidence: 99%
“…Adolphson's proof relies on careful algebraic analysis of the coordinate rings of a collection of varieties whose union is the characteristic variety of the system. Another proof of the holonomicity of an A-hypergeometric system, by Schulze and Walther [SW08], yields a more general result: for a weight vector L from a large family of possibilities, the L-characteristic variety for the L-filtration is a union of conormal varieties and hence has dimension n; holonomicity follows when L = (0, . .…”
Section: Introductionmentioning
confidence: 99%