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arXiv · 2602.08902

The Scrollar Invariants of Curves Mapping to a Hirzebruch Surface

Riccardo Redigolo
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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.

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Riccardo Redigolo. 2026-02-09. The Scrollar Invariants of Curves Mapping to a Hirzebruch Surface. https://arxiv.org/abs/2602.08902

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