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Sep 1, 2022 at 14:22 comment added Misha Verbitsky Z is not a comples subvariety, an u is not closed; it is not har to find varieties which are not close, an the smallest complex subvariety containing them is the whole ambient variety; take, for instance, the graph of exponent in P2
Aug 30, 2022 at 18:57 comment added Tom Goodwillie How can $Z$ be Zariski dense without $U$ being Zariski dense? I confess that I am confused about local-versus-global issues.
Aug 30, 2022 at 17:50 comment added Misha Verbitsky I am not sure this could work; there is nothing prohibiting $Z'=M$, then $U'=M$ as well, your assumption $U=Z\cap U'$ will fail. however, it is not hard to find small-dimensional real analytic subvarieties which are Zariski dense.
Aug 28, 2022 at 19:02 history edited Tom Goodwillie CC BY-SA 4.0
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Aug 28, 2022 at 12:39 history answered Tom Goodwillie CC BY-SA 4.0