I have a question on "Torelli theorems" in algebraic geometry. "Torelli theorems" say about how the period map of a given family of varieties behave. If I understand correctly, global Torelli theorems are the most strong ones and basically classify the varieties you have, that is, the period map is isomorphism. Local Torelli theorems state that the differential of the period map is injective. What do generic Torelli theorem claim then? 



What do generic Torelli theorems claim? 
I would formulate it as follows: global Torelli says that the period map is injective/an immersion (but not necessarily an isomorphism!!), local Torelli says that the period map has injective differential, and generic Torelli says that the period map is generically injective (injective on a Zariski open dense set). 


