The Scrollar Invariants of Curves Mapping to a Hirzebruch Surface
Abstract
In this note we analyse the scrollar invariants of $k:1$ covers of $\mathbb P^1$ that factor through the normalisation of a nodal curve in the $m$-th Hirzebruch surface $\mathbb F_m$. We then give an existence theorem for nodal curves in $\mathbb F_m$ having fixed class and singular locus.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Geometry and complex manifolds
Geometric and Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 February 2026
- Language
- EN
- Document type
- Preprint