Aula Seminario II, Dipartimento di Matematica, Bologna

Abstract.

The moduli space of complete collineations is roughly speaking
a compactification of the space of linear maps between two fixed vector
spaces, in which the boundary divisor is simple normal crossing.
It has been constructed by I. Vainsencher as a sequence of blow-ups
starting from the projective spaces parametrizing matrices modulo scalar
along the Segre variety and its secants varieties in order of
increasing dimension. This space is a spherical wonderful variety.
Exploiting its spherical nature we will investigate its birational
geometry.
We will outline how these notions can be generalized to complete tensors
and their relations with moduli spaces of vector bundles and Hilbert
schemes of rational normal curves.