Boundedness of pluricanonical maps of varieties of general type

Using the techniques of [20] and [10], we prove that certain log forms may be lifted from a divisor to the ambient variety. As a consequence of this result, following [22], we show that: For any positive integer n there exists an integer r(n) such that if X is a smooth projective variety of general type and dimension n, then phi(rKX) : X --> P(H-0(O-X(rK(X)))) is birational for all r >= Nr(n) .