arXiv:1009.3188 New outlook on Mori theory, I from arXiv Front: math.AG by Paolo Cascini, Vladimir Lazic We give a simple and self-contained proof of the finite generation of adjoint rings with big boundaries. As an easy consequence, we show that the canonical ring of a smooth projective variety is finitely generated.
arXiv:1005.0614 New outlook on Mori theory, II from arXiv Front: math.AG by Alessio Corti, Vladimir Lazic In this note we prove that all the fundamental theorems of Mori theory follow quickly from the finite generation of adjoint rings with big boundaries, which was recently proved by a self-contained argument based on extension theorems and induction on the dimension. Thus, we give a new and more efficient organization of higher dimensional algebraic geometry.
nLab page on Mori program