Infinitesimal deformations of some quot schemes, II

TL;DR

This paper explicitly describes all infinitesimal deformations of certain Quot schemes parameterizing torsion quotients of vector bundles over complex projective curves of genus at least 2.

Contribution

It provides a detailed description of the infinitesimal deformation space of Quot schemes for vector bundles on higher genus curves, extending understanding of their deformation theory.

Findings

Explicit description of all deformations of the Quot scheme

Deformation space characterized in terms of the base curve and bundle

Results applicable to moduli problems involving Quot schemes

Abstract

Let $C$ be an irreducible smooth complex projective curve of genus $g$, with $g_C \geqslant 2$. Let $E$ be a vector bundle on $C$ of rank $r$, with $r\geqslant 2$. Let $\mc Q:=\mc Q(E,\,d)$ be the Quot Scheme parameterizing torsion quotients of $E$ of degree $d$. We explicitly describe all deformations of $\mc Q$.