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Feb 20, 2013 at 0:56 comment added J.C. Ottem Yes, that's correct: For Calabi-Yaus it is an open problem even to determine whether the set of CY-families is finite.
Feb 20, 2013 at 0:44 comment added K Kim Thank you for the nice answer. I suppose that Fano threefolds are the only class of threefolds whose explicit classification is known. Calabi-Yau threefolds must be very difficult and general ones are even worse, I guess.
Feb 20, 2013 at 0:40 vote accept K Kim
Feb 20, 2013 at 0:36 history edited J.C. Ottem CC BY-SA 3.0
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Feb 20, 2013 at 0:30 history answered J.C. Ottem CC BY-SA 3.0