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删除10字节 、 2021年1月18日 (一) 00:14
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In [[algebraic geometry]], a [[singular point of an algebraic variety|singularity of an algebraic variety]] is a point of the variety where the [[tangent space]] may not be regularly defined. The simplest example of singularities are curves that cross themselves. But there are other types of singularities, like [[cusp (singularity)|cusps]]. For example, the equation {{math|1= ''y''{{sup|2}} − ''x''{{sup|3}} = 0 }} defines a curve that has a cusp at the origin {{math|1= ''x'' = ''y'' = 0 }}. One could define the {{math|''x''}}-axis as a tangent at this point, but this definition can not be the same as the definition at other points. In fact, in this case, the {{math|''x''}}-axis is a "double tangent."
 
In [[algebraic geometry]], a [[singular point of an algebraic variety|singularity of an algebraic variety]] is a point of the variety where the [[tangent space]] may not be regularly defined. The simplest example of singularities are curves that cross themselves. But there are other types of singularities, like [[cusp (singularity)|cusps]]. For example, the equation {{math|1= ''y''{{sup|2}} − ''x''{{sup|3}} = 0 }} defines a curve that has a cusp at the origin {{math|1= ''x'' = ''y'' = 0 }}. One could define the {{math|''x''}}-axis as a tangent at this point, but this definition can not be the same as the definition at other points. In fact, in this case, the {{math|''x''}}-axis is a "double tangent."
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在代数几何中,'''代数簇的奇点'''是簇中切线空间可能没有规则定义的一点。奇点最简单的例子就是它们自己交叉的曲线。但是还有其他类型的奇点,比如尖点。例如,方程 <math>y_sup(2) x_sup(3) = 0 </math>定义了一条在原点<math> x= y = 0 </math>有一个尖点的曲线。可以将x轴定义为这一点的切线,但这个定义不能与其他点的定义相同。实际上,在这种情况下,-轴是一个“双切线”。
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在代数几何中,'''代数簇的奇点'''是簇中切线空间可能没有规则定义的一点。奇点最简单的例子就是它们自己交叉的曲线。但是还有其他类型的奇点,比如尖点。例如,方程 <math>y^2 − x^3 = 0 </math>定义了一条在原点<math> x= y = 0 </math>有一个尖点的曲线。可以将x轴定义为这一点的切线,但这个定义不能与其他点的定义相同。实际上,在这种情况下,-轴是一个“双切线”。
     
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