Abstract
Let [Formula: see text] be a smooth projective complex curve of genus [Formula: see text]. We investigate the Brill–Noether locus consisting of stable bundles of rank 2 and determinant [Formula: see text] of odd degree [Formula: see text] having at least [Formula: see text] independent sections. This locus possesses a virtual fundamental class. We show that in many cases this class is nonzero, which implies that the Brill–Noether locus is nonempty. For many values of [Formula: see text] and [Formula: see text] the result is best possible. We obtain more precise results for [Formula: see text]. Appendix A contains the proof of a combinatorial lemma which we need.
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