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[几何] 两条代数曲线在p点相交的重数为1,则在p处切线不同

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hbghlyj posted 2024-2-15 18:54 |Read mode
证明如果两条代数曲线在$p$点相交的重数为1,即$I_p(C,D)=1$,则$C$和$D$在$p$处的切线不同

math.stackexchange.com/q/2653030

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original poster hbghlyj posted 2024-2-15 23:00
hbghlyj 发表于 2024-2-15 10:58
我有一个问题:如果 $p\in C\cap D$ 是 $C$ 上的奇点,为什么这意味着 $I_p(C,D)>1$ ? ...
我在algebraiccurves2009.pdf裡居然找到了一模一樣的我没看過這個
Proposition 13 If p ∈ C ∩ D is a singular point of C, then I_p(C, D) > 1.
Proof:

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