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Sep 1, 2010 at 11:44 comment added Jorge Vitório Pereira The answer is still no, $R_1$ is smooth for a generic projection. See Polizzi's answer.
Aug 31, 2010 at 21:08 comment added Makhalan Duff How about if I change the set S to be the points in R_1 which are in the singular locus of the ramification divisor?
Aug 31, 2010 at 20:58 history answered Jorge Vitório Pereira CC BY-SA 2.5