Hodge structure of fibre integrals associated to the afine hypersurface in a torus

Details Hodge structure of fibre integrals associated to the afine hypersurface in a torus Hodge structure of fibre integrals associated to the afine hypersurface in a torus

2002-06-12

arxiv.org/abs/math/0206126v4

Mathematics

Algebraic Geometry

12 pages, minor errors are corrected

Scientific paper

We calculate the fibre integrals of the hypersurface in a torus in the form of their Mellin transforms. Especially, our method works efficiently for an affine hypersurface defined by a so called simpliciable polynomial. The relations between poles of Mellin transforms of fibre integrals, the mixed Hodge structure of the cohomology of the hypersurface, the hypergeometric differential equation and the Euler characteristic of fibres are clarified.

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