On Indices of 1-Forms on Determinantal Singularities

We consider 1-forms on so-called essentially isolated determinantal singularities (a natural generalization of isolated singularities), show how to define analogs of the Poincaré–Hopf index for them, and describe relations between these indices and the radial index. For isolated determinantal singularities, we discuss properties of the homological index of a holomorphic 1-form and its relation to the Poincaré–Hopf index.