Year: 2026
Type: preprint
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 $\mathbb{F}_e$.
Source: arXiv (Cornell University)
Author: Roa-Leguizamón, L.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204870299