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Dickenstein, A.; Felicia Matusevich, L.; Miller, E. "Binomial d-modules" (2010) Duke Mathematical Journal. 151(3):385-429
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Abstract:

We study quotients of the Weyl algebra by left ideals whose generators consist of an arbitrary ℤd-graded binomial ideal I in ℂ[∂ 1 , . . ., ∂ n ] along with Euler operators defined by the grading and a parameter β ∈ ℂ d . We determine the parameters β for which these D-modules (i) are holonomic (equivalently, regular holonomic, when I is standard-graded), (ii) decompose as direct sums indexed by the primary components of I, and (iii) have holonomic rank greater than the rank for generic β. In each of these three cases, the parameters in question are precisely those outside of a certain explicitly described affine subspace arrangement in ℂ d . In the special case of Horn hypergeometric D-modules, when I is a lattice-basis ideal, we furthermore compute the generic holonomic rank combinatorially and write down a basis of solutions in terms of associatedA-hypergeometric functions. This study relies fundamentally on the explicit lattice-point description of the pimary components of an arbitrary binomial ideal in characteristic zero, which we derive in our companion article [DMM]. © 2010 Applied Probability Trust.

Registro:

Documento: Artículo
Título:Binomial d-modules
Autor:Dickenstein, A.; Felicia Matusevich, L.; Miller, E.
Filiación:Departamento de Matemática FCEN, Universidad de Buenos Aires, Buenos Aires, C1428EGA, Argentina
Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104, United States
Department of Mathematics, Texas A and M University, College Station, TX, 77843, United States
Mathematics Department, Duke University, Durham, NC, 27708, United States
Department of Mathematics, University of Minnesota, Minneapolis, MN, 55455, United States
Año:2010
Volumen:151
Número:3
Página de inicio:385
Página de fin:429
DOI: http://dx.doi.org/10.1215/00127094-2010-002
Título revista:Duke Mathematical Journal
Título revista abreviado:Duke Math. J.
ISSN:00127094
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00127094_v151_n3_p385_Dickenstein

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Citas:

---------- APA ----------
Dickenstein, A., Felicia Matusevich, L. & Miller, E. (2010) . Binomial d-modules. Duke Mathematical Journal, 151(3), 385-429.
http://dx.doi.org/10.1215/00127094-2010-002
---------- CHICAGO ----------
Dickenstein, A., Felicia Matusevich, L., Miller, E. "Binomial d-modules" . Duke Mathematical Journal 151, no. 3 (2010) : 385-429.
http://dx.doi.org/10.1215/00127094-2010-002
---------- MLA ----------
Dickenstein, A., Felicia Matusevich, L., Miller, E. "Binomial d-modules" . Duke Mathematical Journal, vol. 151, no. 3, 2010, pp. 385-429.
http://dx.doi.org/10.1215/00127094-2010-002
---------- VANCOUVER ----------
Dickenstein, A., Felicia Matusevich, L., Miller, E. Binomial d-modules. Duke Math. J. 2010;151(3):385-429.
http://dx.doi.org/10.1215/00127094-2010-002