A note on the Brill–Noether loci of small codimension in moduli space of stable bundles

Abstract Let be a smooth projective curve of genus over the field . Let denote the moduli space of stable rank 2 vector bundles on with fixed determinant of degree . Consider the Brill–Noether subvariety of which parameterizes stable vector bundles having at least two linearly independent global sections. In this paper, for generic and , we show that is stably‐rational when , unirational when , and rationally chain connected by Hecke curves, when . We also show triviality of low‐dimensional rational Chow groups of an associated Brill–Noether hypersurface.