Abstract
Hilbert schemes are classical geometric objects first introduced by Grothendieck. In the case of points, they parametrize closed zero-dimensional subschemes in a given ambient space of fixed degree. A natural generalization consists of Hilbert schemes that parametrize nested configurations of points.
In this seminar, I will focus on the problem of understanding when such Hilbert schemes are irreducible, and if they are not, identifying their irreducible components. In particular, I will discuss the interaction between the combinatorics of the nesting and the geometry of the associated Hilbert scheme.
The presentation is based on joint projects with F. Giovenzana, L. Giovenzana, M. Graffeo, S. Monavari, A. Ricolfi, and A. Sammartano.