The minimal model program proposed that the canonical ring of every smooth or mildly singular projective variety was finitely generated. In particular, this was known to imply the existence of a canonical model, a particular birational model of "V" with mild singularities that could be constructed by blowing down "V". When the canonical ring is finitely generated, the canonical model is Proj of the canonical ring. If the canonical ring is not finitely generated, then is not a variety, and so it cannot be birational to "V"; in particular, "V" admits no canonical model.