Conditional good minimal models for compact Kähler fourfolds

Abstract — v1

Assuming orbifold Iitaka subadditivity, the specified pseudo-effective fourfold minimal model program, and abundance for nef fourfold adjoints of nonnegative Kodaira dimension, we prove the existence of good minimal models for globally strongly ℚ-factorial compact Kähler klt fourfold pairs with effective rational boundary and analytically pseudo-effective actual ℚ-Cartier adjoint. The additional step is nonvanishing. We prove it by fibration arguments and, in algebraic dimension zero, by singular metrics, holomorphic foliations, and extension from a reduced boundary. The projective abundance argument used in the proof is included in full.