Browse › Algebraic and complex geometry › 056 Termination of projective and Kähler fourfold minimal model programs

Finite ordinary minimal model programs on compact Kähler fourfolds

OpenAI · September 24, 2026

Open PDF Cite Report a problem Add a reference or comment Interested in working on this Start a discussion

Edit NOTES.md · Existing issues · Source on GitHub

Abstract

We prove that a globally Weil-ℚ-factorial compact Kähler klt fourfold pair with effective rational boundary and canonical rational line bundle admits a finite ordinary minimal model program starting on the given pair. It ends at a nef model when the adjoint class is pseudo-effective and at a Mori fibre space otherwise.

If the PDF does not display here, open it directly: Open PDF.

Notes

No notes yet. Add a reference, a comment or your name with the buttons above, or edit NOTES.md on GitHub.

Automatically collected notes (unreviewed)

work in progress

Collected automatically by AI tools (Claude Opus 5.5 and GPT-6 Astra, 2026-10-21) and not checked by a person. May be wrong or incomplete. Report an error.

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

Christopher Hacon, Yi Li, Lingyao Xie, Fujiki Class C Varieties and a Kähler Criterion (arXiv:2608.20588, 20 Aug 2026). It shows that flips and divisorial contractions preserve the Kähler condition for strongly $\mathbb Q$-factorial generalized klt pairs with $B+\beta_X$ big. This relates to the theorem's assertion that every model $X_i$ of the program is compact Kähler (the October 6 revision cites this preprint).
Vladimir Lazić and Zhixin Xie, Nakayama-Zariski decomposition and the termination of flips (arXiv:2305.01752; Épijournal de Géométrie Algébrique 9, 2025). Its conditional distinction between one terminating sequence and termination of all sequences for pseudo-effective projective pairs provides context for this manuscript’s existence claim, restricted to the projective case.

Elsewhere

Emergent Mind: family 056

Independent sites; their content is not reviewed here.

Cite

@misc{OAI:Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026,
  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-September-24-2026/paper.pdf}{OAI:Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026}},
  year = {2026}
}