Title: Hilbert scheme of points on threefolds

 

Abstract: The Hilbert scheme of $d$ points on a smooth variety $X$, denoted by Hilb$^d(X)$, is an important moduli space with connections to various fields, including combinatorics, enumerative geometry, and complexity theory, to name a few. In this talk, I will introduce this object and review some well-known results when $X$ is a curve or a surface. The main focus of this talk will be on the case when $X$ is a threefold. Specifically, I will present some tantalizing open questions and delve into describing the structure of the smooth points on Hilb$^d(X)$. If time permits, I will also discuss the mildly singular points of this Hilbert scheme.

 

This is all joint work with Joachim Jelisiejew and Alessio Sammartano.

 

Seminar schedule: