On the index of a vector field tangent to a hypersurface with non-isolated zero in the embedding space

Abstract

We give a generalization of an algebraic formula of Gomez-Mont for the index of a vector field with isolated zero in (C^n,0) and tangent to an isolated hypersurface singularity. We only assume that the vector field has an isolated zero on the singularity.

12 pages, minor corrections, accepted for publication in Math. Nachr