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I have always had problems in understanding what people mean when they say "the generalized Theorem of ...". For instance, I seem to understand that there are a few different generazlized Noether-Lefschetz theorems. Can someone list the different versions?

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The set of smooth projective K3 surfaces with Picard number $\rho$ has codimension $\rho−1$ in the moduli space. – J.C. Ottem Apr 15 '12 at 13:26
One generalization is to allow singularities. I believe that Srinivas and Ravindra wrote a paper generalizing the theorem to normal 3 folds. – aginensky Apr 15 '12 at 14:47

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