Semi-simple Carrousels and the Monodromy
[Carrousels semi-simples et Monodromie]
Annales de l'Institut Fourier, Tome 56 (2006) no. 1, pp. 85-100.

Soit U un voisinage ouvert de l’origine dans n+1 et soit f:(𝒰,0)(,0) une fonction analytique complexe. Soit z 0 une forme linéaire générale sur n+1 . Si la courbe polaire relative Γ f,z 0 1 à l’origine est irréductible et le nombre d’intersection est premier, alors cela impose des contraintes très fortes sur la valeur du rang de la n-ième cohomologie de la fibre de Milnor à l’origine. Nous obtenons aussi des résultats intéressants, mais plus faibles quand (Γ f,z 0 1 ·V(f)) 0 n’est pas premier.

Let 𝒰 be an open neighborhood of the origin in n+1 and let f:(𝒰,0)(,0) be complex analytic. Let z 0 be a generic linear form on n+1 . If the relative polar curve Γ f,z 0 1 at the origin is irreducible and the intersection number (Γ f,z 0 1 ·V(f)) 0 is prime, then there are severe restrictions on the possible degree n cohomology of the Milnor fiber at the origin. We also obtain some interesting, weaker, results when (Γ f,z 0 1 ·V(f)) 0 is not prime.

DOI : 10.5802/aif.2173
Classification : 32B99, 32A27, 14E99
Keywords: Carrousel, polar curve, monodromy, Milnor fiber
Mot clés : carrousel, courbe polaire, monodromie, fibre de Milnor
Massey, David B. 1

1 Northeastern University Dept. of Mathematics Boston MA, 02115 (USA)
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Massey, David B. Semi-simple Carrousels and the Monodromy. Annales de l'Institut Fourier, Tome 56 (2006) no. 1, pp. 85-100. doi : 10.5802/aif.2173. http://archive.numdam.org/articles/10.5802/aif.2173/

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