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arXiv · 1012.0618

On Irregular Binomial $D$-modules

María-Cruz Fernández-Fernández·Francisco-Jesús Castro-Jiménez
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Abstract

We prove that a holonomic binomial $D$--module $M_A (I,\beta)$ is regular if and only if certain associated primes of $I$ determined by the parameter vector $\beta\in \CC^d$ are homogeneous. We further describe the slopes of $M_A(I,\beta)$ along a coordinate subspace in terms of the known slopes of some related hypergeometric $D$--modules that also depend on $\beta$. When the parameter $\beta$ is generic, we also compute the dimension of the generic stalk of the irregularity of $M_A(I,\beta)$ along a coordinate hyperplane and provide some remarks about the construction of its Gevrey solutions.

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María-Cruz Fernández-Fernández, Francisco-Jesús Castro-Jiménez. 2010-12-03. On Irregular Binomial $D$-modules. https://arxiv.org/abs/1012.0618

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