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Abstract 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 Tₐ (₄, ₃). In particular, the space of infinitesimal deformations of Q (E, d) is computed. Kempf and Fantechi computed the space of infinitesimal deformations of Q (O₂, d) \, =\, C^ (d) 11, 19.
Biswas et al. (Tue,) studied this question.