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Gómez-Mont, X.; Seade, J.; Verjovsky, A.

The index of a holomorphic flow with an isolated singularity. (English) Zbl 0725.32012

Math. Ann. 291, No. 4, 737-752 (1991).
The index of a holomorphic vector field Z on the germ of a hypersurface \({\mathcal V}\) with an isolated singularity is defined. The index coincides with the Hopf index in the smooth case. Formulae for the index in terms of the ideals defining Z and \({\mathcal V}\) are given. Topological invariance of the index and the Chern class as well as formulae relating global invariants of the Poincaré-Hopf type are proven.
Reviewer: X.Gómez-Mont

Cited in 7 Reviews
Cited in 55 Documents

MSC:

32S05 Local complex singularities
32S25 Complex surface and hypersurface singularities
32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants

Keywords:

index; holomorphic vector field; isolated singularity; Hopf index; Poincaré-Hopf
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Full Text: DOI EuDML

References:

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