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Dec 7, 2022 at 4:27 comment added Sasha It would rather be a similar argument, but different result (there will be less line on $Y$, so the result couldn't be the same). For discussion of a similar question see Lehn, Christian; Lehn, Manfred; Sorger, Christoph; van Straten, Duco. Twisted cubics on cubic fourfolds. J. Reine Angew. Math. 731 (2017), 87--128.
Dec 6, 2022 at 22:13 vote accept CommunityBot
Dec 6, 2022 at 21:53 comment added anon Of course I mean the same result but not the same argument.
Dec 6, 2022 at 20:41 comment added anon Thank you for your answer. What about the case when $Y$ is not smooth? Do we have the same thing?
Dec 6, 2022 at 20:37 history answered Sasha CC BY-SA 4.0