Transform\'ee de Mellin des int\'egrales-fibres associ\'ees aux singularit\'es isol\'ees d'intersection coml\`ete quasihomog\`ene

Abstract

The Mellin transform of fibre integral is calculated for certain isolated singularities of quasihomogeneous complete intersections (especially the unimodal singualrities of the list by Giusti and Wall). We show the property of symmetry between spectra of Gauss-Manin and shed light on the lattice structure of poles of the Mellin transform by means of topological data of the singularity. As an application, Hodge numbers of the Milnor fibre are expressed by counting the spectra of Gauss-Manin.