• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

Homological indices of collections of 1-forms

Bulletin of the London Mathematical Society. 2018. Vol. 50. No. 2. P. 261-273.

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.