On the index of a holomorphic vector field tangent to a singular variety |
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| Authors: | Daniel Lehmann Marcio Soares Tatsuo Suwa |
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| Institution: | (1) GETODIM, CNRS, UA 1407, Université de Montpellier II, 34095 Montpellier cedex, France;(2) Departmento de Matemática, UFMG, 31270-90 Belo Horizonte, Brasil;(3) Department of Mathematics, Hokkaido University, 060 Sapporo, Japan |
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| Abstract: | 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]. |
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