A panoramic view of the geometry of Hilbert schemes of points (and their nested variants)

Abstract

Hilbert schemes are classical geometrical objects first introduced by Grothendieck. In the case of points, they parameterize closed zero-dimensional subschemes of a given ambient space with fixed degree. At the beginning of the seminar, I will review some of the known properties in the classical case. Then, I will discuss how these properties vary if we consider nested configurations of points. In particular, I will focus on the case of double nested configurations, describing the interplay between the combinatorics of the nesting and the geometry of the associated Hilbert scheme. The talk is based on joint projects with F. Giovenzana, L. Giovenzana, M. Graffeo, S. Monavari, A. Ricolfi e A. Sammartano.

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