---
created: 2023-03-31T17:07
updated: 2023-03-31T17:07
---

---
created: 2023-01-23T12:57
aliases: ["rigid"]
---

---

- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [deformation](Unsorted/deformation.md)

---

# rigid

In [HH](HH.md): ![](2023-03-31-100.png)

![](attachments/2023-01-23-rigid.png)


![](attachments/2023-03-05ridigidigid.png)

![](attachments/2023-03-05rigid112.png)
![](attachments/2023-03-05ridigidig.png)

The global monodromy group of an irreducible local system is finite if and only if the corresponding differential equation (with regular singularities) has algebraic solutions. For Gaussian hypergeometric functions, which correspond to rigid local systems of rank 2, the finiteness problem was solved in the 19th century by Schwarz.

More recently [BH89] and [Har94] solved the finiteness problems for the hypergeometric functions ${ }_{\ell} F_{\ell-1}$ and Pochhammer differential equations, respectively.