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nLab
singular point of an algebraic variety

# Contents

## Idea

An algebraic variety $X \hookrightarrow \mathbb{A}^n$ defined as the zero locus of polynomials $\{f^i \in R[x_1, \cdots, x_n]\}$ is *singular* at a point $p$, if the Jacobian matrix of first derivatives at this point has rank lower than at other points.

A variety is called *singular* if it has at least one singular point and *non-singular* if it has none.

## Examples

## References

Last revised on December 27, 2014 at 01:09:59.
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