Irreducibility of Some Quot Schemes on Nodal Curves

Abstract

Let $C$ be an integral projective nodal curve over $\mathbb C$, of arithmetic genus $g \geqslant 2$. Let $E$ be a vector bundle on $C$ of rank $r$ and degree $e$. Let $\textrm{Quot}_{C/\mathbb C}(E,k,d)$ denote the Quot scheme of quotients of $E$ of rank $k$ and degree $d$. We show that $\textrm{Quot}_{C/\mathbb C}(E,k,d)$ is irreducible for $d \gg 0$.