---
date: 2022-02-09 10:14
modification date: Wednesday 9th February 2022 10:14:09
title: arithmetic genus
aliases: [arithmetic genus]

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

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- Tags: 
	- #AG/basics 
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

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# arithmetic genus

The arithmetic genus of a projective variety $\mathrm{X}$ of dimension $r$ is $(-1)^{r}\left(\chi\left(\mathcal{O}_{X}\right)-1\right)$.

![](attachments/Pasted%20image%2020220214101352.png)