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The Segre invariant and Brill-Noether theory on Hirzebruch surfaces
We study the Segre invariant on rank two $H$-stable vector bundles with fixed Chern classes on Hirzebruch surfaces $Σ_{n}$. For each vector bundle on these surfaces, we determine the possible values of the Segre invariant and compute the number of global sections of these bundles and present applica
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