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Given a family of Laurent polynomials, we will construct a morphism betweenits (proper) Gauss-Manin system and a direct sum of associated GKZ systems. Thekernel and cokernel of this morphism are very simple and consist of freeO-modules. The result above enables us to put a mixed Hodge module structure oncertain classes of GKZ systems and shows that they have quasi-unipotentmonodromy.

Laurent Polynomials, GKZ-hypergeometric Systems and Mixed Hodge Modules