Remark: Family 036. Numerical semiampleness and generalized minimal models

Proves numerical semiampleness for nef adjoints $K_X+B+M$ with $K_X+B$ pseudo-effective and $M$ nef rational, for projective klt rational pairs over algebraically closed characteristic-zero fields and smooth compact Kähler rational klt simple-normal-crossing pairs, using Bott–Chern cohomology in the latter case. Separately, projective generalized log canonical rational pairs over such fields admit minimal models for pseudo-effective adjoints and Mori fiber spaces otherwise, with nef b-data fixed.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.