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

摘要

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