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Laurent polynomials, GKZ-hypergeometric systems and mixed Hodge modules

Part of: Families, fibrations Deformations of analytic structures Singularities

Published online by Cambridge University Press:  24 April 2014

Thomas Reichelt
Thomas Reichelt*
Affiliation:
Lehrstuhl VI für Mathematik, Universität Mannheim, Seminargebäude A5, 68131 Mannheim, Germany email thomas.reichelt@math.uni-mannheim.de
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Abstract

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We endow certain GKZ-hypergeometric systems with a natural structure of a mixed Hodge module, which is compatible with the mixed Hodge module structure on the Gauß–Manin system of an associated family of Laurent polynomials. As an application we show that the underlying perverse sheaf of a GKZ-system with rational parameter has quasi-unipotent local monodromy.

Keywords

Gauß–Manin systemhypergeometric D-moduleRadon transformationmixed Hodge module

MSC classification

Secondary: 14D07: Variation of Hodge structures 32S35: Mixed Hodge theory of singular varieties 32S40: Monodromy; relations with differential equations and $D$-modules 32G34: Moduli and deformations for ordinary differential equations (e.g. Knizhnik-Zamolodchikov equation)
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 6 , June 2014 , pp. 911 - 941
Copyright
© The Author 2014 

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