  Homological index of a holomorphic 1-form on a complex analytic variety with
an isolated singular point is an analogue of the usual index of a 1-form on a
non-singular manifold. One can say that it corresponds to the top Chern number
of a manifold. We offer a definition of homological indices for collections of
1-forms on a (purely dimensional) complex analytic variety with an isolated
singular point corresponding to other Chern numbers. We also define new
invariants of germs of complex analytic varieties with isolated singular points
related to "vanishing Chern numbers" at them.
