---
date: 2022-05-25 20:07
modification date: Wednesday 25th May 2022 20:07:33
title: "stable pair"
aliases: [stable pair]
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Last modified date: <%+ tp.file.last_modified_date() %>

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- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
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# stable pair

A par $(X, B)$ where $X$ is a connected [projective variety](projective%20variety) and $B$ is a $\QQ\dash$divisor is **stable** iff

- $(X, B)$ has [slc](Unsorted/slc.md) singularities, and in particular $K_X + B$ is $\QQ\dash$[Cartier](Unsorted/Weil%20divisor.md), 
-  $K_X + B$ is an ample $\QQ\dash$divisor.

![](attachments/2023-03-07stablepair.png)