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created: 2023-03-31T19:20
updated: 2023-03-31T19:20
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---
date: 2022-04-06 04:42
modification date: Wednesday 6th April 2022 04:42:25
title: "stable map"
aliases: [stable map, stable curve]
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Last modified date: <%+ tp.file.last_modified_date() %>

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- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

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# stable map

A map $\gamma:\Sigma \to M$ is stable  iff $\Sigma$ has only finitely many automorphisms compatible with $\gamma$, i.e. each component of $\Sigma$ collapsed to a point by $\gamma$ should have at least three nodes plus marked points ("anchors").

![](2023-03-31-80.png)

In families:
![](attachments/2023-03-31-81.png)
![](attachments/2023-03-31-82.png)

## Stable curves

![](2023-03-31-113.png)


![](2023-03-31-83.png)

![](2023-03-31-84.png)