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Sep 26, 2021 at 5:18 comment added Sergey Guminov Actually, I looked over corollary 1.5 again and now think this is incorrect. Just realized that I, and maybe you too, once again got confused by the notation in the paper. In Corollary 1.5, $Y$ is a special hyperplane section, not the generic one. It's the special sections that must be uniruled, not the generic ones. The generic section is uniruled for a variety of dimension 3 or more, according to Proposition 1.7.
Sep 25, 2021 at 17:00 comment added Sergey Guminov Oh wow, I can't believe I missed that... Thank you so much!
Sep 25, 2021 at 16:58 vote accept Sergey Guminov
Sep 26, 2021 at 5:22
Sep 25, 2021 at 16:12 history answered Daniele A CC BY-SA 4.0