Transcendental Minimal Model Program for Projective Varieties

Abstract

In this article we prove that if $(X,B+{\hat{I}}^2)$ is a projective generalized klt pair such that $B+{\hat{I}}^2$ is big, then $(X,B+{\hat{I}}^2)$ admits a good Minimal Model or Mori fiber space. In particular, this implies Tossati's transcendental base-point-free conjecture for projective manifolds.

Final version. To appear in Algebraic Geometry