---
date: 2022-04-07 19:22
modification date: Thursday 7th April 2022 19:22:49
title: "Deligne-Mumford stack"
aliases: [Deligne-Mumford stack, DM stack, DM]
---

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

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- Tags: 
	- #higher-algebra/stacks 
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

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# Deligne-Mumford stack

![](attachments/2023-03-12steps.png)

- Obstruction to being a DM stack: containing a point whose automorphisms are not etale? Does not obstruct being an [Artin stack](Artin%20stack.md) though. An example involving the modular curve:
  
  ![](attachments/Pasted%20image%2020220407192403.png)

![](attachments/Pasted%20image%2020220807162237.png)