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An algebraic formula for the index of a vector field on an isolated complete intersection singularity

H. -Chr. Graf von Bothmer·W. Ebeling·X. Gomez-Mont
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Abstract

Let (V,0) be a germ of a complete intersection variety in \CC^{n+k}, n>0, having an isolated singularity at 0 and X be the germ of a holomorphic vector field on \CC^{n+k} tangent to V and having on V an isolated zero at 0. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient space \CC^{n+k} we give a formula for the homological index in terms of local linear algebra.

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H. -Chr. Graf von Bothmer, W. Ebeling, X. Gomez-Mont. 2007-11-21. An algebraic formula for the index of a vector field on an isolated complete intersection singularity. https://arxiv.org/abs/math/0601640

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