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Timeline for Bertini's theorem at a fixed point

Current License: CC BY-SA 4.0

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Dec 5 at 14:27 comment added LSpice Re, don't forget that you can (and probably should) post an answer to your own question.
Dec 5 at 14:27 history edited LSpice CC BY-SA 4.0
Proofreading; deleted "Thank you"
Dec 5 at 9:57 comment added MATHQI Oh, I think I know how to do. Consider the projection $ \mathbb{CP}^n\setminus f^{-1}(P)\to \mathbb{CP}^{n}\setminus P \to \mathbb{CP}^{n-1}$. Every point of $\mathbb{CP}^{n-1}$ corresponds with a complex straight line passing through $P$. Use Kleiman's result (Hartshorne chapter 3 Theorem 10.8) for $ f: pt \to \mathbb{CP}^{n-1}$ and $g: CP^{n}\setminus f^{-1}(P) \to \mathbb{CP}^{n-1}$.
Dec 5 at 8:21 history asked MATHQI CC BY-SA 4.0