Ritvik Ramkumar : Hilbert scheme of points on threefolds

Posted by Maya Banks , part of the Algebraic Geometry Seminar.

At

April 6, 2026, 3 p.m.

In

612 SEO

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 focus on the case where X is a threefold, as there are several open questions regarding its singularities. I will describe the structure of the smooth points of this Hilbert scheme and, time permitting, discuss the structure of the mildly singular points. This is all joint (ongoing) work with Joachim Jelisiejew and Alessio Sammartano.