---
date: 2022-08-06 17:35
modification date: Saturday 6th August 2022 17:35:08
title: "automorphisms necessitate stacks"
aliases: [automorphisms necessitate stacks]
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# automorphisms necessitate stacks

![](attachments/Pasted%20image%2020220806173549.png)

![](attachments/Pasted%20image%2020220806173522.png)
![](attachments/Pasted%20image%2020220806173533.png)
![](attachments/Pasted%20image%2020220806173600.png)
Can avoid by passing to the moduli space $\mct_{1, 1}$ of marked elliptic curves to kill automorphisms.

![](attachments/Pasted%20image%2020220806173705.png)

![](attachments/Pasted%20image%2020220806173746.png)
![](attachments/Pasted%20image%2020220806173757.png)