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Log abundance for threefolds in characteristic $p>3$ in numerical dimension one

Principal Theorem 1.1: over an algebraically closed field of characteristic $p>3$ , if $(X,B)$ is a projective log canonical threefold pair with effective $\mathbb Q$ -boundary, $K_X+B$ is $\mathbb Q$ -Cartier, nef and of numerical dimension one, then $K_X+B$ is semiample; neither terminality nor $\mathbb Q$ -factoriality is needed. The companion proves the terminal $\mathbb Q$ -factorial case ( $K_X$ nef with $\nu=1$ gives $\kappa=1$ and semiampleness). Characteristics 2 and 3, numerical dimension zero and higher dimensions are not addressed.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Oct 5, 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: Log abundance for threefolds in characteristic $p>3$ in numerical dimension one · Char p threefold log abundance, nu = 1

Confidence: Not scored

Registry verification: unreviewed · announcement · partial

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VibeMathed
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Unreleased internal OpenAI model
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Named evidence

VibeMathed record: Log abundance for threefolds in characteristic $p>3$ in numerical dimension one

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the introductions and main theorems of both manuscripts were read against the abundance conjecture. lean/docs/035.md does not exist at the pinned commit and formalization.yaml has no entry for either manuscript. The log result uses the companion's cycle obstruction as an essential input, so both papers must hold. Inputs from Xu's nonvanishing and numerical-dimension-two theorems and the positive-characteristic MMP are assumed.

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Log abundance for threefolds in characteristic $p>3$ in numerical dimension one

witness · pending

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

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Companion: Abundance in numerical dimension one for terminal threefolds in positive characteristic

paper · pending

paper link supplied by the VibeMathed registry.

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Companion: Abundance in numerical dimension one for terminal threefolds in positive characteristic evidence for this event

This event attributed to Unreleased internal OpenAI model

Log abundance for threefolds in characteristic $p>3$ in numerical dimension one parent of this event

VibeMathed record: Log abundance for threefolds in characteristic $p>3$ in numerical dimension one evidence for this event

Log abundance for threefolds in characteristic $p>3$ in numerical dimension one evidence for this event

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