{"paper":{"title":"On Irregular Binomial $D$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Francisco-Jes\\'us Castro-Jim\\'enez, Mar\\'ia-Cruz Fern\\'andez-Fern\\'andez","submitted_at":"2010-12-03T01:21:28Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0618","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}