Further examples of stable bundles of rank 2 with 4 sections

TL;DR

This paper constructs new examples of stable rank 2 vector bundles with 4 sections on special curves, revealing that their Brill-Noether loci can have large negative expected dimensions, challenging previous expectations.

Contribution

It provides explicit constructions of stable rank 2 bundles with 4 sections on curves of maximal Clifford index, showing negative expected dimensions of associated loci.

Findings

New stable bundles with 4 sections constructed

Brill-Noether loci can have arbitrarily large negative dimension

Challenges existing expectations about bundle moduli

Abstract

In this paper we construct new examples of stable bundles of rank 2 of small degree with 4 sections on a smooth irreducible curve of maximal Clifford index. The corresponding Brill-Noether loci have negative expected dimension of arbitrarily large absolute value.