Brill--Noether loci of stable rank--two vector bundles on a general curve

TL;DR

This paper provides a straightforward proof of the existence and smoothness of certain Brill--Noether loci for stable rank-2 vector bundles on general curves, with applications to the Hilbert scheme of scrolls.

Contribution

It offers a simplified proof of the existence of smooth components of Brill--Noether loci for rank-2 bundles on general curves, advancing understanding of their geometric properties.

Findings

Existence of smooth components of Brill--Noether loci confirmed

Components have the expected dimension

Applications to Hilbert schemes of scrolls

Abstract

In this note we give an easy proof of the existence of generically smooth components of the expected dimension of certain Brill--Noether loci of stable rank 2 vector bundles on a curve with general moduli, with related applications to Hilbert scheme of scrolls.