---
date: 2022-02-11 10:40
modification date: Friday 11th February 2022 10:40:22
title: nef divisor
aliases: [nef divisor, nef, numerically effective.]

---

Last modified date: <%+ tp.file.last_modified_date() %>

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- Tags: 
	- #todo/untagged
- Refs:
	- <https://people.sissa.it/~bruzzo/notes/toric.pdf#page=36&zoom=160,-97,23>
- Links:
	- [minimal model program](minimal%20model%20program)
	- [ample](Unsorted/ample.md)
	- [Cartier divisor](Unsorted/Weil%20divisor.md)
	- [normal](Unsorted/normalization.md)
	- [[numerically equivalent]]
	- [[Mori cone]]

---

# nef divisor
![](attachments/Pasted%20image%2020220928230629.png)


A line bundle $\mcl$ on $X$ is **nef** iff for all [integral subvarieties](integral%20subvarieties) $Y \subseteq X$, $\qty{\prod_{i\leq \dim Y} \mcl} Y \geq 0$.

Note that 

- [ample](ample) implies nef, 
- nef plus nef is nef
- nef tensor [[ample]] is [[ample]].

$\mcl$ is nef iff its restriction to every curve is positive.

![](attachments/Pasted%20image%2020210627222319.png)


![](attachments/Pasted%20image%2020220531034929.png)

![](attachments/Pasted%20image%2020220928230651.png)