Soit un voisinage ouvert de l’origine dans et soit une fonction analytique complexe. Soit une forme linéaire générale sur . Si la courbe polaire relative 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 -ième cohomologie de la fibre de Milnor à l’origine. Nous obtenons aussi des résultats intéressants, mais plus faibles quand n’est pas premier.
Let be an open neighborhood of the origin in and let be complex analytic. Let be a generic linear form on . If the relative polar curve at the origin is irreducible and the intersection number is prime, then there are severe restrictions on the possible degree cohomology of the Milnor fiber at the origin. We also obtain some interesting, weaker, results when is not prime.
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}, pages = {85--100}, publisher = {Association des Annales de l'institut Fourier}, volume = {56}, number = {1}, year = {2006}, doi = {10.5802/aif.2173}, mrnumber = {2228681}, zbl = {1102.32013}, language = {en}, url = {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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