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: