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Fujita's freeness conjecture

Theorem 1.1: for every smooth connected complex projective variety $X$ of dimension $n\ge1$ and every ample line bundle $L$ , $K_X+(n+1)L$ is generated by global sections; hence $K_X+mL$ is globally generated for all $m\ge n+1$ , even when $L$ itself is not. The bound is sharp. The method minimises an exponential average of normalised section orders over bases and weighted monomial valuations, then lifts sections with Fujita's discrepancy-and-vanishing mechanism. It does not prove the very-ampleness conjecture ( $m\ge n+2$ ) or point separation.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 23, 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: Fujita's freeness conjecture

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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Attribution

VibeMathed
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Unreleased internal OpenAI model
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SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Fujita's freeness conjecture

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the abstract, introduction and Theorem 1.1 were read against Fujita's conjecture as the manuscript cites it. The proof was not refereed. No Lean formalization: the manuscript is not in lean/formalization.yaml and lean/docs/038.md does not exist at the pinned commit. Scope the paper itself states: only the freeness (global generation) part is proved, not separation of points or tangents and not the very-ampleness half of Fujita's conjecture. Readers should know a previous claimed proof (Chan, arXiv 2411.07129) was withdrawn in November 2024; the manuscript cites that withdrawal. A brief web search on 7 October 2026 found no public dispute of this manuscript.

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Fujita's freeness conjecture

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Fujita 1987, Adv. Stud. Pure Math. 10

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problem-record link supplied by the VibeMathed registry.

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Lineage and corrections

Fujita 1987, Adv. Stud. Pure Math. 10 evidence for this event

This event attributed to Unreleased internal OpenAI model