An algebraic formula for the index of a vector field on an isolated complete intersection singularity
Abstract
Let (V,0) be a germ of a complete intersection variety in n+k, n>0, having an isolated singularity at 0 and X be the germ of a holomorphic vector field on 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 n+k we give a formula for the homological index in terms of local linear algebra.
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