PORTUGALIAE MATHEMATICA Vol. 63, No. 2, pp. 173226 (2006) 

Hypergeometric periods for a tame polynomialClaude SabbahUMR 7640 du CNRS, Centre de Mathématiques Laurent Schwartz,École polytechnique, F91128 Palaiseau cedex  FRANCE Email: sabbah@math.polytechnique.fr URL: http://www.math.polytechnique.fr/\ sabbah Abstract: We analyse the GaussManin 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 Hodgetype results analogous to those existing for germs of isolated hypersurface singularities. Classification (MSC2000): 14D07, 14D05, 32G20, 32S40. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2006 Sociedade Portuguesa de Matemática
