Some examples of rank-2 Brill-Noether loci

TL;DR

This paper constructs specific examples of rank-2 Brill-Noether loci with unusual properties on general curves, highlighting new phenomena in algebraic geometry and connecting to recent advances in Mercat's conjecture.

Contribution

It provides explicit examples of rank-2 Brill-Noether loci with unexpected features, including in genus 6 and higher, and relates these to recent proofs of Mercat's conjecture.

Findings

Examples of rank-2 Brill-Noether loci with unexpected properties

Connections to recent proof of Mercat's conjecture in rank 2

New phenomena observed in higher genus cases

Abstract

In this paper, we construct some examples of rank-2 Brill-Noether loci with "unexpected" properties on general curves. The key example is in genus 6, but we also have interesting examples in rank 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.