Brill-Noether theory and non-special scrolls

TL;DR

This paper explores the Brill-Noether theory of sub-line bundles in rank-two vector bundles on curves, linking it to the geometry of unisecant curves on non-special scrolls, using degeneration methods.

Contribution

It establishes new connections between Brill-Noether theory and the geometry of scrolls, providing novel degeneration-based results for general curves.

Findings

Characterization of sub-line bundles in stable rank-two bundles

Relation between Brill-Noether theory and unisecant curves on scrolls

Degeneration techniques applied to study scroll geometry

Abstract

In this paper we study the Brill-Noether theory of sub-line bundles of a general, stable rank-two vector bundle on a curve C with general moduli. We relate this theory to the geometry of unisecant curves on smooth, non-special scrolls with hyperplane sections isomorphic to C. Most of our results are based on degeneration techniques.