Abstract
LetV be a germ at 0 ∈C 2,n≥3, of hypersurface with an isolated singularity at 0. In this paper we prove that the maximal number of germs of vector fields inV *=V−0, which are linearly independent in all points ofV * is two. In the casesn=3,4 and of quasi homogeneous hypersurfaces (∀n≥3), we prove that this number is one.
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Dedicated to the memory of R. Mañé
This research was partially supported by Pronex.
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Neto, A.L. Holomorphic rank of hypersurfaces with an isolated singularity. Bol. Soc. Bras. Mat 29, 145–161 (1998). https://doi.org/10.1007/BF01245871
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DOI: https://doi.org/10.1007/BF01245871