Infinitesimal Deformations of Some Quot Schemes

Let E be a vector bundle on a smooth complex projective curve C of genus at least two. Let Q(E,d) be the Quot scheme parameterizing the torsion quotients of E of degree d. We compute the cohomologies of the tangent bundle TQ(E,d). In particular, the space of infinitesimal deformations of Q(E,d) is computed. Kempf and Fantechi computed the space of infinitesimal deformations of Q( OC,d)\,=\, C⁽ᵈ⁾ [ 11, 19].