---
date: 2022-04-05 23:42
modification date: Wednesday 6th April 2022 21:19:42
title: "Hurwitz space"
aliases: [Hurwitz space, branched cover, branched covers, branched, Hurwitz]
---

Last modified date: <%+ tp.file.last_modified_date() %>

---

- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [moduli of curves](Unsorted/moduli%20stack%20of%20elliptic%20curves.md)
	- [homological stability MOC](Unsorted/homological%20stability%20MOC.md)

---


# Hurwitz space

![](attachments/Pasted%20image%2020220502172219.png)

![](attachments/Pasted%20image%2020220208152904.png)
![](attachments/Pasted%20image%2020220208152938.png)

![](attachments/Pasted%20image%2020220406211929.png)
![](attachments/Pasted%20image%2020220406211942.png)
Exihibits [homological stability](Unsorted/homological%20stability%20MOC.md), related to [orbifolds](Unsorted/orbifold.md):
![](attachments/Pasted%20image%2020220406212335.png)
![](attachments/Pasted%20image%2020220406212434.png)

Definition in terms of [configuration spaces](Unsorted/configuration%20space.md) and the [character variety](character%20variety)
![](attachments/Pasted%20image%2020220406213740.png)

As a moduli space:
![](attachments/Pasted%20image%2020220406213813.png)