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date: 2022-04-05 23:42
aliases: ["semistable degeneration"]
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Last modified: `=this.file.mday`

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# semistable degeneration


A semistable degeneration $X\to \AA^1$: a [proper morphism](proper morphism.md) where the fibers away from zero are smooth and the fiber over zero is an SNC divisor in the total space:


![Pasted image 20210515182208](attachments/Pasted%20image%2020210515182208.png)

# Semistability in geometry
![](attachments/Pasted%20image%2020220317211706.png)
![](attachments/Pasted%20image%2020220317211833.png)

![](attachments/2023-03-13semistable-reduction.png)