Some examples of rank-2 Brill–Noether loci

In this paper, we construct some examples of rank-2 Brill–Noether loci with “unexpected” properties on general curves. The key examples are in genus 6, but we also have interesting examples in genus 5 and in higher genus. We relate some of our results to the recent proof of Mercat’s conjecture in rank 2 by Bakker and Farkas.