---
created: 2022-04-05T23:42
updated: 2024-01-01T23:13
---


---
date: 2022-04-06 04:42
modification date: Thursday 12th May 2022 21:52:29
title: "Torelli"
aliases: [Torelli]
---

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

---

- Tags: 
	- #todo/untagged
- Refs:
	- For [K3](K3%20surfaces.md): <https://math.uchicago.edu/~sfilip/public_files/lectures_k3_dynamics.pdf#page=23&zoom=auto,-200,513>
- Links:
	- #todo/create-links 

---

# Torelli

Idea: a non-singular projective [algebraic curve](algebraic%20curve.md)  $C\slice k$ for any $k=\bar k$ is determined by its Jacobian variety $\Jac(C) \in \Ag$.
Equivalently, there is a [period map](period%20map) $P: \Mg \to \Ag$ which is injective on [geometric points](Unsorted/geometric%20fiber.md).

For K3s:
![](attachments/Pasted%20image%2020220807161616.png)