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Jun 14, 2020 at 3:19 comment added Ben Wieland Note that you need the projective/algebraic hypothesis, because the Hopf surface is a counterexample. All Hopf surfaces are diffeomorphic, preserving the subvarieties, because they don't have a lot of subvarieties. (They don't have 1-d subvarieties whose intersection is 0-d.)
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Jun 12, 2020 at 20:57 answer added Jason Starr timeline score: 10
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