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Finite ordinary minimal model programs on compact Kähler fourfolds

OpenAI · October 6, 2026

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Abstract

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.

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Possibly relevant literature (found by the agent, not checked)

Makoto Enokizono, Kenta Hashizume, On termination of minimal model program for log canonical pairs on complex analytic spaces (arXiv:2501.03531, v2 8 Dec 2025). It studies termination of lc MMPs in the complex analytic setting, which relates to the paper's use of relative analytic MMP inputs and special termination for its ordinary negative-ray programs.
Vladimir Lazić and Zhixin Xie, Nakayama-Zariski decomposition and the termination of flips (arXiv:2305.01752; Épijournal de Géométrie Algébrique 9, 2025). Its conditional passage from one terminating sequence to all sequences for pseudo-effective projective pairs provides a comparison with the projective case of this version’s claim about every maximal ordinary program.

Elsewhere

Emergent Mind: family 056

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Cite

@misc{OAI:Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026,
  author = {{OpenAI}},
  title = {{Finite ordinary minimal model programs on compact K{\"a}hler fourfolds}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026/paper.pdf}{OAI:Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026}},
  year = {2026}
}