Infinitesimal deformations of some quot schemes, II

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