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Oct 6, 2010 at 11:25 comment added damiano Actually, if a non-singular surface is a product of curves and is non-singular, then it is minimal, so it is not a blow up of a non-singular surface. This same argument might give some ideas of how to proceed in general... maybe!
Oct 6, 2010 at 11:18 history answered damiano CC BY-SA 2.5