---
date: 2022-04-05 23:42
modification date: Saturday 9th April 2022 17:27:31
title: "divisor"
aliases: [divisors]
---

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

---
- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- Types of divisors:
		- [big](Unsorted/big.md)
		- [nef divisor](Unsorted/nef%20divisor.md)
		- [Weil divisor](Weil%20divisor.md)
		- [Cartier divisor](Cartier%20divisor)
		- [Ample divisor](Ample%20divisor.md)
		- [irreducible divisor](Unsorted/irreducible%20divisor.md)
	- [O(D) for D a divisor](O(D)%20for%20D%20a%20divisor.md)
	- [Unsorted/linearly equivalent divisors](Unsorted/linearly%20equivalent%20divisors.md)
	- [Weil reciprocity](Unsorted/Weil%20reciprocity.md)
	- [Neron Severi](Unsorted/Neron%20Severi.md)

---

# divisor

## Notes

- Definition: a $\ZZ\dash$ linear combinations of codimension 1 subvarieties.
- A **principal divisor** is one arising from a meromorphic function


![](attachments/Pasted%20image%2020220214093632.png)

## Function fields

![](attachments/Pasted%20image%2020220316133751.png)
![](attachments/Pasted%20image%2020220316133803.png)

# Hyperplane sections

![](attachments/Pasted%20image%2020220830181410.png)

# Support

![](attachments/Pasted%20image%2020220913171551.png)