Semi-simple Carrousels and the Monodromy

Massey, David B.

doi:10.5802/aif.2173

Semi-simple Carrousels and the Monodromy
[Carrousels semi-simples et Monodromie]

Massey, David B.¹

¹ Northeastern University Dept. of Mathematics Boston MA, 02115 (USA)

Annales de l'Institut Fourier, Tome 56 (2006) no. 1, pp. 85-100.

Résumé
Abstract

Soit $U$ un voisinage ouvert de l’origine dans $ℂ^{n + 1}$ et soit $f : (𝒰, 0) \to (ℂ, 0)$ une fonction analytique complexe. Soit $z_{0}$ une forme linéaire générale sur $ℂ^{n + 1}$ . 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 $(Γ_{f, z_{0}}^{1} {\cdot V (f))}_{0}$ n’est pas premier.

Let $𝒰$ be an open neighborhood of the origin in $ℂ^{n + 1}$ and let $f : (𝒰, 0) \to (ℂ, 0)$ be complex analytic. Let $z_{0}$ be a generic linear form on $ℂ^{n + 1}$ . If the relative polar curve $Γ_{f, z_{0}}^{1}$ at the origin is irreducible and the intersection number $(Γ_{f, z_{0}}^{1} {\cdot V (f))}_{0}$ 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 $(Γ_{f, z_{0}}^{1} {\cdot V (f))}_{0}$ is not prime.

MR Zbl

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

Affiliations des auteurs :

Massey, David B. ¹

¹ Northeastern University Dept. of Mathematics Boston MA, 02115 (USA)

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     title = {Semi-simple {Carrousels} and the {Monodromy}},
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     pages = {85--100},
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     volume = {56},
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     year = {2006},
     doi = {10.5802/aif.2173},
     zbl = {1102.32013},
     mrnumber = {2228681},
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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. https://www.numdam.org/articles/10.5802/aif.2173/

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