The Segre invariant and Brill-Noether theory on Hirzebruch surfaces

Source abstract

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 applications to Brill-Noether Theory.