---
date: 2022-04-22 22:52
modification date: Friday 22nd April 2022 22:52:20
title: "log discrepancy"
aliases: [discrepancy, crepant, discrepancy divisor, log discrepancy, terminal, canonical, log terminal, log canonical, canonical, canonical singularity, klt, ]
created: 2023-05-31T13:08
updated: 2023-05-31T13:09
---

---
- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [exceptional divisor](Unsorted/blowup.md)
	- [simply normal crossings divisor](Unsorted/simple%20normal%20crossings.md)
	- [Cartier divisor](Unsorted/Weil%20divisor.md)

---

# canonical singularities (toric)

![](attachments/2023-02-27canonc.png)

![](2023-05-31.png)
![](2023-05-31-1.png)

![](2023-05-31-2.png)

# log discrepancy

![](attachments/Pasted%20image%2020221019193253.png)

- A map is **crepant** if the pullback of the [canonical divisor](canonical%20divisor.md) is again the canonical divisor.
- The discrepancy divisor of a crepant resolution $h : Y \to X$ is zero by definition.

![](attachments/Pasted%20image%2020220422225222.png)

![](attachments/Pasted%20image%2020220422225526.png)


![](attachments/Pasted%20image%2020221005213455.png)
![](attachments/Pasted%20image%2020221005213509.png)