English

The Scrollar Invariants of Curves Mapping to a Hirzebruch Surface

Algebraic Geometry 2026-02-10 v1 Commutative Algebra

Abstract

In this note we analyse the scrollar invariants of k:1k:1 covers of P1\mathbb P^1 that factor through the normalisation of a nodal curve in the mm-th Hirzebruch surface Fm\mathbb F_m. We then give an existence theorem for nodal curves in Fm\mathbb F_m having fixed class and singular locus.

Keywords

Cite

@article{arxiv.2602.08902,
  title  = {The Scrollar Invariants of Curves Mapping to a Hirzebruch Surface},
  author = {Riccardo Redigolo},
  journal= {arXiv preprint arXiv:2602.08902},
  year   = {2026}
}