---
title: Brill-Noether theorem
aliases: [Brill-Noether theorem, Brill-Noether theory]
created: 2022-02-08T17:29
updated: 2023-04-01T09:20
---


# Brill-Noether theorem

Broadly speaking, the theory is about studying the space of line bundles of a fixed degree having a fixed number of linearly independent global sections.

![](attachments/Pasted%20image%2020220208172933.png)
![](attachments/Pasted%20image%2020220208172913.png)