OpenAI · 056-04 · 2026-10-06 · Algebraic and complex geometry
Finite ordinary minimal model programs on compact Kähler fourfolds
preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026
Family 056. Termination of fourfold minimal model programs.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves termination of every existing generalized log canonical flip sequence on globally Weil -factorial compact Kähler fourfolds, with rational boundary, fixed rational analytically nef b-data, and projective small flip diagrams with the prescribed ample signs. Also proves termination of arbitrary permitted minimal model programs for projective log canonical fourfolds with rational boundary in characteristic zero.
We prove that every maximal ordinary negative-ray program starting from a compact Kähler klt fourfold pair with effective rational boundary in the global Weil-divisor ℚ-factorial category terminates. It ends at a nef model when the adjoint is pseudo-effective and at a projective Mori fibre space otherwise.
Preprint source and Lean scope
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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.