Examples of hypergeometric twistor 𝒟-modules

Castaño Domínguez, Alberto; Reichelt, Thomas; Sevenheck, Christian

doi:10.2140/ant.2019.13.1415

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Examples of hypergeometric twistor $\mathcal{D}$-modules

Alberto Castaño Domínguez, Thomas Reichelt and Christian Sevenheck

Vol. 13 (2019), No. 6, 1415–1442

DOI: 10.2140/ant.2019.13.1415

Abstract

We show that certain one-dimensional hypergeometric differential systems underlie objects of the category of irregular mixed Hodge modules, which was recently introduced by Sabbah, and compute the irregular Hodge filtration for them. We also provide a comparison theorem between two different types of Fourier–Laplace transformation for algebraic integrable twistor $D$ -modules.

Keywords

D-modules, irregular Hodge filtration, twistor D-modules, Fourier–Laplace transformation, hypergeometric D-modules

Mathematical Subject Classification 2010

Primary: 14F10

Secondary: 32C38

Milestones

Received: 17 July 2018

Revised: 28 January 2019

Accepted: 8 March 2019

Published: 18 August 2019

Authors

Alberto Castaño Domínguez
Instituto de Matemáticas Universidade de Santiago de Compostela Spain	Fakultät für Mathematik Technische Universität Chemnitz Chemnitz Germany

Thomas Reichelt
Mathematisches Institut Universität Heidelberg Heidelberg Germany

Christian Sevenheck
Fakultät für Mathematik Technische Universität Chemnitz Chemnitz Germany

Vol. 13, No. 6, 2019