Automorphisms of the generalized quot schemes

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Given a compact connected Riemann surface X of genus g ≥ 2, and integers r≥ 2, dₚ > 0 and dz > 0, in BDHW, a generalized quot scheme Qₓ(r,dₚ,dz) was introduced. Our aim here is to compute the holomorphic automorphism group of Qₓ(r,dₚ,dz). It is shown that the connected component of Aut(Qₓ(r,dₚ,dz)) containing the identity automorphism is PGL(r,C). As an application of it, we prove that if the generalized quot schemes of two Riemann surfaces are holomorphically isomorphic, then the two Riemann surfaces themselves are isomorphic.