Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 63, No. 2, pp. 173-226 (2006)

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Hypergeometric periods for a tame polynomial

Claude Sabbah

UMR 7640 du CNRS, Centre de Mathématiques Laurent Schwartz,
École polytechnique, F--91128 Palaiseau cedex -- FRANCE
E-mail: sabbah@math.polytechnique.fr
URL: http://www.math.polytechnique.fr/\ sabbah

Abstract: We analyse the Gauss--Manin system of differential equations --- and its Fourier transform --- attached to regular functions satisfying a tameness assumption on a smooth affine variety over $\mathbb{C}$ (e.g. tame polynomials on $\mathbb{C}^{n+1}$). We give a solution to the Birkhoff problem and prove Hodge-type results analogous to those existing for germs of isolated hypersurface singularities.

Classification (MSC2000): 14D07, 14D05, 32G20, 32S40.

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Electronic version published on: 7 Mar 2008.

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