Journal of Singularities
volume 9 (2014), 206-218
Received 23 February 2012. Received in revised form 23 January 2013.
We introduce a local invariant for a vector field v on a complete intersection V with an isolated singularity as the residue of the relevant Chern class of the ambient tangent bundle by a frame consisting of v and some natural meromorphic vector fields associated with defining functions of V. We then show that the residue coincides with the GSV-index as well as the virtual index of v so that it provides another interpretation of these indices. As an application, we give an algebraic formula for the GSV-indices of holomorphic vector fields on singular curves.
Department of Mathematics
Sapporo 060-0810, Japan