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.