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Résumé :
Monodromie d'une famille d'hypersurfaces
Soit une variété projective complexe lisse irréductible de dimension m+1 , plongée dans un espace projectif. Soit un sous-schéma fermé de , et soit un entier positif tel que I_Z,Y() soit engendré par ses sections globales. Fixons un entier d+1 , et supposons que le diviseur général X |H^0(Y,I_Z,Y(d))| soit lisse. Désignons par H^m(X;Q)_Z^van le quotient de par la cohomologie de et par les classes des composantes irréductibles de de dimension . Dans cet article, nous prouvons que la représentation de monodromie sur pour la famille des diviseurs lisses est irréductible.

Mots-clefs : Variété projective lisse, système linéaire, théorie de Lefschetz, monodromie, singularité isolée, fibration de Milnor

Abstract:
Let be an (m+1) -dimensional irreducible smooth complex projective variety embedded in a projective space. Let be a closed subscheme of , and be a positive integer such that I_Z,Y() is generated by global sections. Fix an integer d+1 , and assume the general divisor X |H^0(Y,I_Z,Y(d))| is smooth. Denote by H^m(X;Q)_Z^van the quotient of by the cohomology of and also by the cycle classes of the irreducible components of dimension of . In the present paper we prove that the monodromy representation on for the family of smooth divisors is irreducible.

Keywords: Complex projective variety, linear system, Lefschetz theory, monodromy, isolated singularity, Milnor fibration

Class. math. : 14B05, 14C20, 14C21, 14C25, 14D05, 14M10, 32S55

ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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