Geometric invariants for certain class of semi-Fredholm Hilbert modules

Shibananda Biswas
Abstract
We describe a sheaf model for a class of semi-Fredholm Hilbert modules over the polynomial ring in m-variables. This sheaf is easily seen to be coherent. We use this model to to give a decomposition of the reproducing kernel and extract several unitary invariants for the corresponding Hilbert module. On the way we describe the joint kernel of the adjoint of the multiplication operator in terms of generators of the module. Explicit computations of these invariants in several examples will be given.