zbMATH — the first resource for mathematics

Un cas d’indépendance des courants polaires de \(f^{\lambda+m}f^{\lambda-m}\). (A case of independence of polar currents of \(f^{\lambda+m}f^{\lambda-m})\). (French) Zbl 0727.32014
We show that for a germ \(f\) of holomorphic functions at 0 in \({\mathbb{C}}^{n+1}\) such that \(f\) is in its jacobian ideal \(J_ f=(\partial f/\partial z_ j)_{0\leq j\leq n}\), the polar currents of type (1,1) of the meromorhic extension of \(f^{\lambda+m}f^{\lambda-m}df\wedge d\bar f\wedge \square\) are linearly independent. As application of this result, we give a generalization of the classical E. Borel theorem.
Reviewer: A.Jeddi
32S05 Local complex singularities
Full Text: DOI Numdam EuDML
[1] BARLET (D.). - Développement asymptotique des fonctions obtenues par intégration sur les fibres, Invent. Math., t. 68, 1982, p. 129-174. Zbl0508.32003 MR84a:32021 · Zbl 0508.32003 · doi:10.1007/BF01394271 · eudml:142929
[2] BARLET (D.) et MAIRE (H.M.). - Asymptotic expansion of complex integrals via Mellin transform, J. Funct. Anal., t. 83, 1989, p. 233-257. Zbl0707.32003 MR91c:32006 · Zbl 0707.32003 · doi:10.1016/0022-1236(89)90020-7
[3] MILNOR (J.). - Singular points of complex hypersurfaces. - Ann. of Math. Studies 61, Princeton, 1968. Zbl0184.48405 MR39 #969 · Zbl 0184.48405
[4] RUBENTHALER (H.). - La surjectivité de l’application moyenne pour les espaces préhomogènes., J. Funct. Anal., t. 60, 1985, p. 80-94. Zbl0557.43007 MR86h:22015 · Zbl 0557.43007 · doi:10.1016/0022-1236(85)90059-X
[5] SAITO (K.). - Quasihomogene isolierte Singularitäten von Hyperflachen, Invent. Math., t. 14, 1971, p. 123-142. Zbl0224.32011 MR45 #3767 · Zbl 0224.32011 · doi:10.1007/BF01405360 · eudml:142107
[6] TREVES (F.). - Locally convex spaces and linear partial differential equations. - Springer Verlag, Berlin/Heidelberg/New York, 1967. Zbl0152.32104 MR36 #6986 · Zbl 0152.32104
[7] ZARISKI (O.) et SAMUEL (P.). - Commutative algebra. - Van Nostrand, 1967.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.