Some recent results on the punctual Quot schemes

TL;DR

This paper surveys recent advances in understanding the invariants of punctual Quot schemes parameterizing torsion quotients of vector bundles over complex curves, highlighting new theoretical insights.

Contribution

It compiles and discusses recent results on invariants of Quot schemes, offering a comprehensive overview of current progress in the field.

Findings

New formulas for invariants of Quot schemes

Connections between Quot schemes and curve geometry

Recent computational techniques for invariants

Abstract

Let $C$ be a smooth projective curve defined over the field of complex numbers. Let $E$ be a vector bundle on $C$, and fix an integer $d\geqslant 1$. Let $\mc Q:={\rm Quot}(E,d)$ be the Quot Scheme which parameterizes all torsion quotients of $E$ of degree $d$. In this article, we survey some recent results on various invariants of $\mc Q$.