Termination of flips for projective log canonical fourfolds with rational boundary
Theorem 1.1: for a projective lc pair of dimension four with rational boundary over an algebraically closed field of characteristic zero, every negative extremal ray at every stage has its contraction and, when birational, a positive model; every permitted program has finitely many birational steps for every sequence of choices; and every maximal program ends at a nef adjoint or a Mori fibre space. Proved over by a weighted difficulty with a topological branch estimate, then transferred to all such fields. Not shown: real boundaries, generalized pairs in the projective setting, any dimension above four, or semiampleness of the nef endpoint without the release's log abundance result. The Kahler companions prove termination for generalized lc flips with projective small diagrams on globally Weil Q-factorial compact Kahler fourfolds, a four-dimensional rational form of Hacon-Xie's Conjecture 1.15.
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Occurred: Sep 24, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Termination of flips for projective log canonical fourfolds with rational boundary · Termination of lc fourfold flips
Confidence: Not scored
Registry verification: unreviewed · announcement · partial
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Unreleased internal OpenAI model
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Termination of flips for projective log canonical fourfolds with rational boundary parent of this event
Theorem 1.1: for a projective lc pair of dimension four with rational boundary over an algebraically closed field of characteristic zero, every negative extremal ray at every stage has its contraction and, when birational, a positive model; every permitted program has finitely many birational steps for every sequence of choices; and every maximal program ends at a nef adjoint or a Mori fibre space. Proved over by a weighted difficulty with a topological branch estimate, then transferred to all such fields. Not shown: real boundaries, generalized pairs in the projective setting, any dimension above four, or semiampleness of the nef endpoint without the release's log abundance result. The Kahler companions prove termination for generalized lc flips with projective small diagrams on globally Weil Q-factorial compact Kahler fourfolds, a four-dimensional rational form of Hacon-Xie's Conjecture 1.15. parent of this event
VibeMathed record: Termination of flips for projective log canonical fourfolds with rational boundary evidence for this event
Termination of flips for projective log canonical fourfolds with rational boundary evidence for this event
Companion: Termination of generalized log canonical flips on compact Kahler fourfolds evidence for this event
Companion: Termination of generalized-canonical flips on compact Kahler fourfolds evidence for this event
Companion: Finite ordinary minimal model programs on compact Kahler fourfolds (Oct 5) evidence for this event
Companion: Finite ordinary minimal model programs on compact Kahler fourfolds (Sep 24) evidence for this event
Revised edition (October 6, 2026): Finite ordinary minimal model programs on compact Kähler fourfolds evidence for this event
Revised edition (October 6, 2026): Termination of generalized-canonical flips on compact Kähler fourfolds evidence for this event
Revised edition (October 7, 2026): Termination of generalized log canonical flips on compact Kähler fourfolds evidence for this event
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