  If (V,0) is an isolated complete intersection singularity and X a holomorphic
vector field tangent to V one can define an index of X, the so called GSV
index, which generalizes the Poincare-Hopf index. We prove that the GSV index
coincides with the dimension of a certain explicitely constructed vector space,
if X is deformable in a certain sense and V is a curve. We also give a
sufficient algebraic criterion for X to be deformable in this way. If one
considers the real analytic case one can also define an index of X which is
called the real GSV index. Under the condition that X has the deformation
property, we prove a signature formula for the index generalizing the
Eisenbud-Levine Theorem.
