We give a new and self-contained proof of the finite generation of adjoint rings with big boundaries. As a consequence, we show that the canonical ring of a smooth projective variety is finitely generated.
Paolo Cascini. Vladimir Lazić. "New outlook on the Minimal Model Program, I." Duke Math. J. 161 (12) 2415 - 2467, 15 September 2012. https://doi.org/10.1215/00127094-1723755