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Hypergeometric periods for a tame polynomial. (English) Zbl 1113.14011
The author considers the Gauss-Manin system (GMS) of differential equations attached to a regular function satisfying a tameness assumption on a smooth affine variety over $${\mathbb C}$$ (e.g. a tame polynomial on $${\mathbb C}^{n+1}$$, i.e. a polynomial $$f$$ for which one has $$\| \partial f\| \geq \varepsilon$$ outside some compact $$K$$ for some $$\varepsilon >0$$). The author considers also the Fourier transform of the GMS. He solves the Birkhoff problem and proves Hodge-type results analogous to those concerning germs of isolated hypersurface singularities.

MSC:
 14D07 Variation of Hodge structures (algebro-geometric aspects) 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.) 32G20 Period matrices, variation of Hodge structure; degenerations 32S40 Monodromy; relations with differential equations and $$D$$-modules (complex-analytic aspects)
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