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date: 2022-06-02 16:10
modification date: Thursday 2nd June 2022 16:10:32
title: "examples of varieties"
aliases: [examples of varieties]
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# examples of varieties

![](attachments/Pasted%20image%2020220602161034.png)

- $V(xy-t)$, a family of hyperbolas degenerating to a pair of lines.
- $V(x^2-ty)$, a family of parabolas degenerating to a single line with multiplicity 2.
- The [twisted cubic](Unsorted/twisted%20cubic.md):
  ![](attachments/Pasted%20image%2020220603133330.png)
- Rational normal curves:
  ![](attachments/Pasted%20image%2020220603133343.png)
- Conifolds $V(xy-zw) \subset \CC^4$.
	- Toric with torus $V \intersect (\CC^*)^4 = \ts{(x,y,z,xyz\inv)}$.
- Generalized conifolds $V(xy - z^{n_1} w^{n_2})$.