Curves, K3 surfaces, abelian varieties, ... is there more context to the question or is this just a "big list"?
– MattApr 10 '11 at 19:09

All affine varieties, trivially! are you assuming $k$ to be perfect? and is the motivation stemming from Deligne-Illusie's famous paper?
– SGPApr 10 '11 at 21:58

In addition to affine varieties, curves, K3 surfaces, abelian varieties, have anything else which statisfy the liftability? The $k$ may be perfect or even algebraically closed.
– UniverseApr 11 '11 at 10:57

Is there a particular variety or class of varieties you want to be liftable? Perhaps that would give you a better answer.
– Karl SchwedeApr 11 '11 at 11:15

I want to know as much as possible class of schemes or varieties(especially projective)， which can be lift to $W_2(k)$. Does any toric varieties always liftable?
– UniverseApr 11 '11 at 12:50