Moduli spaces of bundles and Hilbert schemes of scrolls over -gonal curves

The aim of this paper is twofold. We first strongly improve our previous main result Choi et al. (Proc Am Math Soc 146(8):3233-3248, 2018, Theorem 3.1), concerning classification of irreducible components of the Brill-Noether locus parametrizing rank 2 semistable vector bundles of suitable degrees d, with at least d-2g+4 independent global sections, on a general -gonal curve C of genus g. We then uses this classification to study several properties of the Hilbert scheme of suitable surface scrolls in projective space, which turn out to be special and stable.