nLab
singular point of an algebraic variety

Contents

Idea

An algebraic variety X𝔸 nX \hookrightarrow \mathbb{A}^n defined as the zero locus of polynomials {f iR[x 1,,x n]}\{f^i \in R[x_1, \cdots, x_n]\} is singular at a point pp, 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. See the history of this page for a list of all contributions to it.