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Jun 13, 2011 at 9:26 vote accept Vivek Shende
Jun 13, 2011 at 8:38 history edited Sándor Kovács CC BY-SA 3.0
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Jun 13, 2011 at 8:37 comment added Sándor Kovács I see. That seems to be OK as long as you only want it set-theoretically. My problem was that for instance in the first case I think you can get twice the point, but not the point itself. In general, it may be hard to get the point with multiplicity less than its multiplicity on $Y$, but (again) this does not seem to be an issue for you.
Jun 13, 2011 at 8:06 comment added Vivek Shende Hi Sandor, thanks for answering. In the question, I only meant set-theoretic intersection; but I guess it looks like your second answer answers that too. For a disc just passing through the vertex, I thought you should just take any general disc so the intersection with the $Y$ is finitely many points, then shrink to avoid those points. Does that not work?
Jun 13, 2011 at 5:26 history answered Sándor Kovács CC BY-SA 3.0