A Note On the moduli space of rank two vector bundles on Hirzebruch surfaces

L. Roa-Leguizamón

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arXiv · 2608.30236

A Note On the moduli space of rank two vector bundles on Hirzebruch surfaces

L. Roa-Leguizamón

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Abstract

The aim of this paper is to study the Segre invariant for rank $2$ vector bundles on Hirzebruch surfaces $\mathbb{F}_e$, $e \geq 0$. We give necessary conditions in order to determine what numbers can appear as the Segre Invariant of a rank $2$ vector bundle on $\mathbb{F}_e$ with fixed Chern classes. We compute a bound of the dimensions of the strata whenever are non-empty. Finally, we present applications to Brill-Noether Theory and describe differences between moduli spaces under change of polarization for rank $2$ vector bundles on $\mathbb{F}_e$.

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L. Roa-Leguizamón. 2026-08-31. A Note On the moduli space of rank two vector bundles on Hirzebruch surfaces. https://arxiv.org/abs/2608.30236

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