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Mar 9, 2019 at 6:16 comment added abx @Aknazar Kazhymurat: No, I don't know any reference, in fact I don't know any example of what you mention — but I am not an expert.
Mar 8, 2019 at 13:19 comment added abx Since $X$ is affine, any proper subvariety of $X'$ is contained in a fiber of the blow up, which has dimension $\leq n-1$ if $X$ and $Y$ are smooth.
Mar 8, 2019 at 12:25 comment added rori what if we assume that $X$ and $Y$ are smooth?
Mar 8, 2019 at 11:59 history answered Sasha CC BY-SA 4.0