# Bounds on the Dimension of the Brill-Noether Schemes of Rank Two Bundles

## TL;DR

This paper establishes upper bounds on the dimension of Brill-Noether loci for rank two vector bundles on algebraic curves, providing insights into their geometric structure and implications for moduli spaces.

## Contribution

It introduces new upper bounds on the dimension of Brill-Noether schemes for rank two bundles, advancing understanding of their geometric properties.

## Key findings

- Derived explicit upper bounds for the dimension of Brill-Noether loci.
- Analyzed consequences of these bounds on the structure of moduli spaces.
- Provided theoretical insights into the geometry of rank two vector bundles.

## Abstract

The aim of this note is to find upper bounds on the dimension of Brill-Noether locus' inside the moduli space of rank two vector bundles on a smooth algebraic curve. We deduce some consequences of these bounds.