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Apr 7, 2022 at 20:30 comment added Jana @EvgenyShinder and abx: Thanks for your comments.
Apr 7, 2022 at 16:39 comment added abx See What's the cohomology ring structure of a blow-up?.
Apr 7, 2022 at 11:32 comment added Evgeny Shinder By projection formula this vanishing holds if $\pi_*(E^i) = 0$ in Chow groups; this must be the case when $i$ is less than codimension of the center of the blowup. On the other hand, when $n = 3$, $i = 2$ and we blow up a curve, the answer is not necessary zero (it is roughly degree of the curve).
Apr 7, 2022 at 10:12 history asked Jana CC BY-SA 4.0