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15 February 2010 Binomial D-modules
Alicia Dickenstein, Laura Felicia Matusevich, Ezra Miller
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Duke Math. J. 151(3): 385-429 (15 February 2010). DOI: 10.1215/00127094-2010-002


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 βCd. 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. This study relies fundamentally on the explicit lattice-point description of the primary components of an arbitrary binomial ideal in characteristic zero, which we derive in our companion article [DMM]


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Alicia Dickenstein. Laura Felicia Matusevich. Ezra Miller. "Binomial D-modules." Duke Math. J. 151 (3) 385 - 429, 15 February 2010.


Published: 15 February 2010
First available in Project Euclid: 8 February 2010

zbMATH: 1205.13031
MathSciNet: MR2605866
Digital Object Identifier: 10.1215/00127094-2010-002

Primary: 32C38 , 33C70
Secondary: 13N10 , 14M25

Rights: Copyright © 2010 Duke University Press


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Vol.151 • No. 3 • 15 February 2010
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