Let be an -dimensional irreducible smooth complex projective variety embedded in a projective space. Let be a closed subscheme of , and be a positive integer such that is generated by global sections. Fix an integer , and assume the general divisor is smooth. Denote by 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.
Soit une variété projective complexe lisse irréductible de dimension , plongée dans un espace projectif. Soit un sous-schéma fermé de , et soit un entier positif tel que soit engendré par ses sections globales. Fixons un entier , et supposons que le diviseur général soit lisse. Désignons par 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.
Keywords: complex projective variety, linear system, Lefschetz theory, monodromy, isolated singularity, Milnor fibration
Mot clés : variété projective lisse, système linéaire, théorie de Lefschetz, monodromie, singularité isolée, fibration de Milnor
@article{ASENS_2009_4_42_3_517_0, author = {Di Gennaro, Vincenzo and Franco, Davide}, title = {Monodromy of a family of hypersurfaces}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {517--529}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 42}, number = {3}, year = {2009}, doi = {10.24033/asens.2101}, mrnumber = {2543331}, zbl = {1194.14016}, language = {en}, url = {http://www.numdam.org/articles/10.24033/asens.2101/} }
TY - JOUR AU - Di Gennaro, Vincenzo AU - Franco, Davide TI - Monodromy of a family of hypersurfaces JO - Annales scientifiques de l'École Normale Supérieure PY - 2009 SP - 517 EP - 529 VL - 42 IS - 3 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/asens.2101/ DO - 10.24033/asens.2101 LA - en ID - ASENS_2009_4_42_3_517_0 ER -
%0 Journal Article %A Di Gennaro, Vincenzo %A Franco, Davide %T Monodromy of a family of hypersurfaces %J Annales scientifiques de l'École Normale Supérieure %D 2009 %P 517-529 %V 42 %N 3 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/asens.2101/ %R 10.24033/asens.2101 %G en %F ASENS_2009_4_42_3_517_0
Di Gennaro, Vincenzo; Franco, Davide. Monodromy of a family of hypersurfaces. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 42 (2009) no. 3, pp. 517-529. doi : 10.24033/asens.2101. http://www.numdam.org/articles/10.24033/asens.2101/
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