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| HAL : hal-00124034, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Sur les germes de fonctions holomorphes a lieu singulier de dimension 1: le cas général. |
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| Daniel Barlet 1, 2 |
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| (12/01/2007) |
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| The main goal of this article is to extend the results of [B.06] to a general holomorphic germ $f$ with a one dimensional singular locus at the origine of $\Bbb C ^{n+1}, n ≥ 2$. To obtain this generalization it is enough to prove that some nice properties of the cohomology sheaves of the formal completion "in $f$" of the sub-complex given by holomorphic forms annihilated by $\wedge df$ of the holomorphic de Rham complex, obtained under the assumption (HH) in [B.06] are true in general. We also compute explicitely some examples and show the relationship between the $(a,b)$-connexion introduced previously and integrals "à la Malgrange" on vanishing cycles. |
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| 1 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine |
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| 2 : | Institut Universitaire de France (IUF) |
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Ministère de l'Enseignement Supérieur et de la Recherche Scientifique |
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| Analyse et Géométrie complexe |
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| Domaine | : | Mathématiques/Variables complexes |
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| Hypersurface – Non Isolated Singularity – Vanishing Cycles – (a – b)-modules. |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00124034, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00124034 | |
| oai:hal.archives-ouvertes.fr:hal-00124034 | |
| Contributeur : Daniel Barlet | |
| Soumis le : Vendredi 12 Janvier 2007, 10:39:00 | |
| Dernière modification le : Vendredi 12 Janvier 2007, 11:14:00 | |
