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May 4, 2022 at 17:54 vote accept user45397
May 4, 2022 at 11:57 comment added user45397 @EvgenyShinder Thanks for the answer.
May 4, 2022 at 7:39 comment added Evgeny Shinder In the parameter space of all lines passing through $p$ (this is a projective space), interesecting a codimension two subvariety away from $p$ is a proper closed condition. Hence we are asking whether this projective space can be covered by countably many proper closed subvarieties, which is not the case. Thus there exsits a line with the required properties.
May 3, 2022 at 21:03 answer added Will Sawin timeline score: 2
May 3, 2022 at 20:27 answer added pinaki timeline score: 1
May 3, 2022 at 16:40 comment added user45397 @Wojowu Yes, the underlying field is $\mathbb{C}$. I have made it explicit in the question.
May 3, 2022 at 16:39 history edited user45397 CC BY-SA 4.0
added 13 characters in body
May 3, 2022 at 14:05 comment added Wojowu Are you working over $\mathbb C$? This is obviously false over countable fields.
May 3, 2022 at 12:51 history asked user45397 CC BY-SA 4.0