Artículo

Dickenstein, A.; Matusevich, L.F.; Miller, E. "Binomial D-modules" (2010) Duke Mathematical Journal. 151(3):1-13
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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 βεCd 2 Cd. 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 Cd. 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 associated A-hypergeometric functions. Fundamental in this study is an explicit lattice point description of the primary components of an arbitrary binomial ideal in characteristic zero, which we derive from a characteristic-free combinatorial result on binomial ideals in affine semigroup rings. Effective methods can be derived for the computation of primary components of arbitrary binomial ideals and series solutions to classical Horn systems.

Registro:

Documento: Artículo
Título:Binomial D-modules
Autor:Dickenstein, A.; Matusevich, L.F.; Miller, E.
Filiación:Departamento de Matemática, Fcen, Universidad de buenos aires, Buenos Aires, 1428, Argentina
Department Of Mathematics, University Of Pennsylvania, Philadelphia, PA 19104, United States
Department Of Mathematics, University Of Minnesota, Minneapolis, MN 55455, United States
Department of Mathematics, Texas AandM University, College Station, TX 77843, United States
Año:2010
Volumen:151
Número:3
Página de inicio:1
Página de fin:13
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_p1_Dickenstein

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Citas:

---------- APA ----------
Dickenstein, A., Matusevich, L.F. & Miller, E. (2010) . Binomial D-modules. Duke Mathematical Journal, 151(3), 1-13.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00127094_v151_n3_p1_Dickenstein [ ]
---------- CHICAGO ----------
Dickenstein, A., Matusevich, L.F., Miller, E. "Binomial D-modules" . Duke Mathematical Journal 151, no. 3 (2010) : 1-13.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00127094_v151_n3_p1_Dickenstein [ ]
---------- MLA ----------
Dickenstein, A., Matusevich, L.F., Miller, E. "Binomial D-modules" . Duke Mathematical Journal, vol. 151, no. 3, 2010, pp. 1-13.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00127094_v151_n3_p1_Dickenstein [ ]
---------- VANCOUVER ----------
Dickenstein, A., Matusevich, L.F., Miller, E. Binomial D-modules. Duke Math. J. 2010;151(3):1-13.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00127094_v151_n3_p1_Dickenstein [ ]