Irreducibility of Some Quot Schemes on Nodal Curves

Abstract

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

Comments are welcome. Changes: Corrected some typos. Some details are added to the strategy of the proof in the introduction