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

Published 2006-01-26, updated 2007-11-21Version 3

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.