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Mar 2, 2013 at 10:41 vote accept Kim
Feb 23, 2013 at 19:46 comment added roy smith I agree with Dan. What is often proved for generic Torelli (also called "degree one Torelli"), is only that some proper extension of the map has a regular value with a single preimage, or that some blowup of some proper extension has such a value. A related approach argues that a generic source point is determined by the image of the differential there. In all these approaches, a precise description of a dense Zariski open set on which the map must then be injective often remains unknown. (Some people say "infinitesimal Torelli" instead of "local Torelli" for "injective differential".)
Feb 23, 2013 at 11:56 history answered Dan Petersen CC BY-SA 3.0