---
title: "Kuranishi spaces"
aliases: [Kuranishi spaces, Kuranishi space, Kuranishi chart, Kuranishi charts]
created: 2022-04-30T18:37
updated: 2023-04-02T12:29
---

---

- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [orientation](Unsorted/orientable.md)
	- [virtual fundamental class](Unsorted/virtual%20fundamental%20class.md)

---

Idea: a Kuranishi family is a germ of a moduli space.

# Kuranishi spaces

![](2023-04-02-4.png)

See Fukaya-Oh-Ohta-Ono.

![](attachments/Pasted%20image%2020220517131229.png)

# Kuranishi charts

![](attachments/Pasted%20image%2020220325225338.png)
![](attachments/Pasted%20image%2020220325225346.png)

Relation to [orbifolds](Unsorted/orbifold.md):
![](attachments/Pasted%20image%2020220325225433.png)

# For M_g

Involves **framing** of curve:

![](attachments/Pasted%20image%2020220325230500.png)
![](attachments/Pasted%20image%2020220325230511.png)