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 $d \gg 0$.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Polynomial and algebraic computation
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Publication date
- 8 July 2026
- Language
- EN