2002/06/12 by Susumu Tanabé, Tanabé, Susumu
Mathematics · #14M10 #32S25 #32S40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.CV #msc:14M10 #msc:32S25 #msc:32S40
paper · pdf · doi:10.48550/arxiv.math/0206126
12 pages, minor errors are corrected
openalex publication_date 2002/06/12 · arxiv created 2004/06/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.