Transcendental Minimal Model Program for Projective Varieties

In this article we prove that if $(X,B+\beta)$ is a projective generalized klt pair such that $B+\beta$ is big, then $(X,B+\beta)$ admits a good Minimal Model or Mori fiber space.

In particular, this implies Tossati's transcendental base-point-free conjecture for projective manifolds.