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IRREGULAR HODGE FILTRATION OF SOME CONFLUENT HYPERGEOMETRIC SYSTEMS

Part of: Analytic spaces (Co)homology theory

Published online by Cambridge University Press:  24 May 2019

Alberto Castaño Domínguez Open the ORCID record for Alberto Castaño Domínguez [Opens in a new window]  and
Christian Sevenheck
Alberto Castaño Domínguez
Affiliation:
Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782Santiago de Compostela, Spain (alberto.castano@usc.es)
Christian Sevenheck
Affiliation:
Fakultät für Mathematik, Technische Universität Chemnitz, 09107Chemnitz, Germany (christian.sevenheck@mathematik.tu-chemnitz.de)
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Abstract

We determine the irregular Hodge filtration, as introduced by Sabbah, for the purely irregular hypergeometric ${\mathcal{D}}$-modules. We obtain, in particular, a formula for the irregular Hodge numbers of these systems. We use the reduction of hypergeometric systems from GKZ-systems as well as comparison results to Gauss–Manin systems of Laurent polynomials via Fourier–Laplace and Radon transformations.

Keywords

D-modulesirregular Hodge filtrationhypergeometric systemstwistor D-modules

MSC classification

Primary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 32C38: Sheaves of differential operators and their modules, $D$-modules
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 2 , March 2021 , pp. 627 - 668
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Copyright
© Cambridge University Press 2019

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Footnotes

The authors are partially supported by the project SISYPH: ANR-13-IS01-0001-01/02 and DFG grant SE 1114/5-1.

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