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Termination of generalized-canonical flips on compact Kähler fourfolds

OpenAI · October 6, 2026

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Abstract

Every sequence of generalized-canonical flips on compact Kähler fourfolds with rational boundary and fixed rational analytically nef b-divisor terminates when the small morphisms are projective. We prove this for normal globally Weil ℚ-factorial models with boundary coefficients less than one, allowing exceptional log discrepancies equal to one. No scaling rule or pseudo-effectivity assumption is required. The theorem applies to existing projective small diagrams with the specified opposite ample signs.

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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 hypothesis that the successive models are compact Kähler, and to the paper's comparison with Das–Hacon–Păun, who assume this.
Valery Alexeev, Christopher Hacon and Yujiro Kawamata, Termination of (many) 4-dimensional log flips (arXiv:math/0605137, 2006). Termination for projective klt fourfold pairs whose negative adjoint is numerically equivalent to an effective divisor provides a comparison with the manuscript’s ordinary projective canonical specialization, under an additional numerical hypothesis.

Elsewhere

Emergent Mind: family 056

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Cite

@misc{OAI:Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026,
  author = {{OpenAI}},
  title = {{Termination of generalized-canonical flips on compact K{\"a}hler fourfolds}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026/termination-generalized-terminal-flips-compact-kahler-fourfolds.pdf}{OAI:Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026}},
  year = {2026}
}