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Sep 3, 2021 at 13:52 comment added Wenlong @JasonStarr Thank you. I hope it doesn't annoy you but what if we restrict to Calabi-Yau threefolds?
Sep 3, 2021 at 13:49 vote accept Wenlong
Sep 3, 2021 at 13:42 comment added Jason Starr @Wenlong Welcome new contributor. That is still negative. Fix a line in projective $3$-space. For every positive integer $d$ you can find a smooth degree-$d$ hypersurface containing the line. The normal bundle is an invertible sheaf on the line of degree $2-d$, which is arbitrarily negative as $d$ increases.
Sep 3, 2021 at 13:28 comment added Wenlong What if we ask the ambient variety to have non-negative Kodaira dimension?
Sep 3, 2021 at 13:20 history answered Sasha CC BY-SA 4.0