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