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Sep 20, 2014 at 6:55 comment added naf It is not possible to have $X_p$ smooth away from codimension two: in the relative dimension $1$ case this amounts to asking if you can have $X_p$ to be smooth and this is not always possible, e.g. for elliptic curves.
Sep 19, 2014 at 15:55 history asked Roman Fedorov CC BY-SA 3.0