Semi-simple Carrousels and the Monodromy  [ Carrousels semi-simples et Monodromie ]
Annales de l'Institut Fourier, Tome 56 (2006) no. 1, p. 85-100
Soit U un voisinage ouvert de l’origine dans ℂ n+1 et soit f:(𝒰,0)→(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 ·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)→(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 ·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 : https://doi.org/10.5802/aif.2173
Classification:  32B99,  32A27,  14E99
Mots clés: carrousel, courbe polaire, monodromie, fibre de Milnor 
@article{AIF_2006__56_1_85_0,
     author = {Massey, David B.},
     title = {Semi-simple Carrousels and the Monodromy},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {56},
     number = {1},
     year = {2006},
     pages = {85-100},
     doi = {10.5802/aif.2173},
     mrnumber = {2228681},
     zbl = {1102.32013},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2006__56_1_85_0}
}

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://www.numdam.org/item/AIF_2006__56_1_85_0/

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