On Irregular Binomial $D$-modules

Details On Irregular Binomial $D$-modules On Irregular Binomial $D$-modules

2010-12-03

arxiv.org/abs/1012.0618v2

Mathematics

Algebraic Geometry

17 pages, Theorems 4.8 and 5.1, Examples 4.5 and 4.6, some remarks and some references added

Scientific paper

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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