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Characteristic cycles and Gevrey series solutions of $A$-hypergeometric systems

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arxiv 1902.04339 v1 pith:K5UB43KJ submitted 2019-02-12 math.AG

Christine Berkesch , María-Cruz Fernández-Fernández This is my paper · ORCID
classification math.AG
keywords characteristiccyclesgevreyhypergeometricresultssystemanalyzeapply
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abstract

We compute the $L$-characteristic cycle of an $A$-hypergeometric system and higher Euler-Koszul homology modules of the toric ring. We also prove upper semicontinuity results about the multiplicities in these cycles and apply our results to analyze the behavior of Gevrey solution spaces of the system.

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  1. Gevrey and formal Nilsson solutions of $A$-hypergeometric systems

    math.AG 2019-08 accept novelty 7.0 of 10

    For all complex parameters, Gevrey solutions of A-hypergeometric systems along coordinate subspaces embed into formal Nilsson solutions; with a cone condition the spaces are equal and have dimension vol(τ).

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