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Transformée de Mellin des intégrales-fibres associées aux singularités isolées d'intersection complète quasihomogènes. (Mellin Transform of Fibre Integrals Associated to Isolated Complete Intersection Singularities)

Published online by Cambridge University Press:  04 December 2007

Susumu Tanabé
Susumu Tanabé
Affiliation:
Independent University of Moscow, Bol'shoj Vlasievskij pereulok 11, Moscow 121002, Russia. E-mail: [email protected] Max Planck Institut für Mathematik, Vivatsgasse 7, Bonn, D-53111, Germany. E-mail: [email protected]
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Abstract

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The Mellin transform of the fibre integral is calculated for certain quasihomogeneous isolated complete intersection singularities (above all, unimodal singularities of the list by Giusti and Wall). We show the symmetry property of the Gauss–Manin spectra (Theorem 3.1) and shed light on the lattice structure of the poles of the Mellin transform that are expressed by means of some topological data of the singularities (Theorem 4.3, Theorem 5.2). As an application of these results, we express the Hodge number of the fibre in terms of the Gauss–Manin spectra.

Keywords

Gauss–Manin connexioncomplete intersectionHodge structure
Type
Research Article
Information
Compositio Mathematica , Volume 130 , Issue 2 , January 2002 , pp. 119 - 160
Copyright
© 2002 Kluwer Academic Publishers