Extensions of line bundles and Brill--Noether loci of rank-two vector bundles on a general curve

TL;DR

This paper investigates the structure of Brill-Noether loci for rank-two vector bundles on general curves, describing typical members as extensions of line bundles, thus advancing understanding of vector bundle moduli.

Contribution

It provides new descriptions of Brill-Noether loci components for rank-two bundles as extensions of line bundles on general curves.

Findings

Characterization of general members as line bundle extensions

Descriptions of specific Brill-Noether loci components

Enhanced understanding of vector bundle moduli on curves

Abstract

In this paper we study Brill-Noether loci for rank-two vector bundles and describe the general member of some components as suitable extensions of line bundles.