---
date: 2022-04-07 20:11
modification date: Thursday 7th April 2022 20:11:41
title: "smooth points"
aliases: [smooth points, smooth locus, smooth, smooth point, singular point, singular points, singular, singularity, double normal crossings, pinch point]
---

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

---
- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [Milnor fiber](Milnor%20fiber)
	- [ADE singularity](Unsorted/ADE%20singularities.md)
	- [du Val singularities](du%20Val%20singularities)

---

# smooth points

- Curve singularities are often studied via their associated [Puiseux series](Puiseux%20series) and [Newton polygons](Newton%20polygons)
![](attachments/Pasted%20image%2020220526141111.png)

![](attachments/Pasted%20image%2020220407201144.png)

![](attachments/Pasted%20image%2020220407225612.png)

![](attachments/Pasted%20image%2020220407225739.png)

# Singular subschemes

![](attachments/Pasted%20image%2020220410171545.png)

# Isolated singularities

![](attachments/Pasted%20image%2020220410211906.png)

# Cone singularities

![](attachments/Pasted%20image%2020220410184136.png)


## Nodes

![](attachments/Pasted%20image%2020220410212210.png)

# Quadratic singularities

![](attachments/Pasted%20image%2020220424142705.png)
![](attachments/Pasted%20image%2020220424142726.png)
![](attachments/Pasted%20image%2020220424142746.png)
![](attachments/Pasted%20image%2020220424142802.png)

# Examples

![](attachments/Pasted%20image%2020220528012655.png)