Hilbert schemes of points and applications

TL;DR

This thesis explores Hilbert schemes of points, presenting mathematical results, open problems, and historical context, serving as a comprehensive resource for understanding their properties and applications.

Contribution

It provides new mathematical insights into Hilbert schemes of points along with open problems and historical perspectives, enriching the existing literature.

Findings

Mathematical properties of Hilbert schemes of points

Identification of open problems in the field

Historical overview of Hilbert schemes

Abstract

The thesis concerns Hilbert schemes of points and apart from mathematical results, contains small open problems and history sections, see the introduction for more details. The thesis has not been edited since 2017, see first page for more information. It is shared "as is" (in the language of GPL) solely due/thanks to several people who decided to refer to it.