 On the other hand, the problem of termination—proving that there can be no infinite sequence of flips—is still open in dimensions greater than 3.If formula_20 is a morphism, and "K" is the canonical bundle of "X", then the relative canonical ring of "f" is
and is a sheaf of graded algebras over the sheaf formula_22 of regular functions on "Y".The blowup 
of "Y" along the relative canonical ring is a morphism to "Y".