Abstract
This text is a survey on my recent work [B.04] on some holomorphic germs having a one dimensional singular locus. An analogous of the Brieskorn module of an isolated singularity is defined and a finiteness theorem is proved using Kashiwara’s constructibility theorem. A bound for the (finite dimensional) torsion is also obtained. Non existence of torsion is proved for curves (reduced or not) an this property is stable by “Thom-Sebastiani” adjunction of an isolated singularity. This provides a lot of examples in any dimension where our formula r = μ(f)+v(f) generalizing the Milnor number formula, is valid.
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Références
Barlet, D. Théorie des (a, b)-modules I, in Complex Analysis and Geometry, Plenum Press, (1993), p. 1–43.
Barlet, D. Sur certaines singularités non isolées d’hypersurfaces I, preprint Institut E. Cartan 2004/ n o 03, 47 pages.
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Malgrange, B. Intégrale asymptotique et monodromie, Ann. Sc. Ec. Norm. Sup. 7 (1974), p. 405–430.
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Barlet, D. (2006). Quelques Résultats sur Certaines Fonctions à Lieu Singulier de Dimension 1. In: Brasselet, JP., Ruas, M.A.S. (eds) Real and Complex Singularities. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7776-2_3
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DOI: https://doi.org/10.1007/978-3-7643-7776-2_3
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