Transform\'ee de Mellin des int\'egrales- fibres associ\'ees \`a l'intersection compl\`ete non-d\'eg\'en\'er\'ee

Abstract

Mellin transform of fibre integral is calculated for certain classes of non-degenerate affine complete intersections. The lattice structure of the poles of the Mellin transform is clarified by means of the mixed Hodge structure of the affine variety in question. One establishes the relation of the fibre integral with the hypergeometric function of Horn and that of Gel'fand-Kapranov-Zelevinski. As an application we prove an hypothesis proposed by Berglund, Candelas et altri on the mirror symmetry.