Given a compact connected Riemann surface $X$ of genus $g \geq 2$, and integers $r\geq 2$, $d_p > 0$ and $d_z > 0$, in \cite{ BDHW}, a generalized quot scheme ${ \mathcal Q}_X(r,d_p,d_z)$ was introduced. Our aim here is to compute the holomorphic automorphism group of ${ \mathcal Q}_X(r,d_p,d_z)$. It is shown that the connected component of $\text{ Aut}( { \mathcal Q}_X(r,d_p,d_z))$ containing the identity automorphism is $\text{ PGL}(r,{ \mathbb C})$. 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.
Categories: math.AG math-ph math.MP
