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On the index of a holomorphic vector field tangent to a singular variety

1995; Springer Science+Business Media; Volume: 26; Issue: 2 Linguagem: Inglês

10.1007/bf01236993

2317-6679

Daniel Lehmann, Márcio G. Soares, Tatsuo Suwa,

Algebraic Geometry and Number Theory

In this article we define and compute an index for a holomorphic vector field on a (possibly singular) subvariety of a complex manifold, provided the subvariety is a local complete intersection. This index reduces to the usual Poincaré-Hopf index in case the subvariety is smooth, and is equal more generally to the index defined in [GSV] and [SS].