Vol. 13, No. 6, 2019

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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