The strong hyperkahler SYZ conjecture

Theorem 1.1: if $c_1(L)\ne0$ , $c_1(L)$ is in the closure of the Kahler cone and $q_X(c_1(L))=0$ , then $L$ is semiample: some $L^m\simeq f^*A$ for a surjective connected-fibre map $f:X\to B$ onto a normal projective $n$ -dimensional $B$ with $A$ ample, every fibre component Lagrangian of dimension $n$ . Corollary 1.2: in each dimension there are finitely many deformation types with $b_2\ge5$ . Corollary 1.3 (projective $X$ , via the companion): $B\simeq\mathbb P^n$ . Not shown: existence of a nef isotropic class on a given $X$ , or anything for $b_2\le4$ in the finiteness corollary.

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: The strong hyperkahler SYZ conjecture · Strong hyperkahler SYZ conjecture

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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VibeMathed
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Unreleased internal OpenAI model
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Named evidence

VibeMathed record: The strong hyperkahler SYZ conjecture

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 and Corollaries 1.2-1.3 of 'The strong hyperkahler SYZ conjecture' were read against Verbitsky's Conjecture 1.7 as cited. The proof (a degeneration to a flat cylinder in logarithmic coordinates, a special Lagrangian torus by the Zhang-McLean method, hyperkahler rotation to a nonprojective manifold, Greb-Lehn-Rollenske, and Soldatenkov-Verbitsky deformation back to the given pair) was not refereed. No Lean formalization. The theorem has no restriction on dimension, deformation type or second Betti number; the finiteness corollary for deformation types with b2 >= 5 also uses Engel-Filipazzi-Greer-Mauri-Svaldi. The paper does not use the release's contested log abundance results.

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The strong hyperkahler SYZ conjecture

witness · pending

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

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Same family: Projective-space bases of Lagrangian fibrations

paper · pending

paper link supplied by the VibeMathed registry.

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Verbitsky 2010, Hyperkahler SYZ conjecture and semipositive line bundles (GAFA)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

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Same family: Projective-space bases of Lagrangian fibrations evidence for this event

Verbitsky 2010, Hyperkahler SYZ conjecture and semipositive line bundles (GAFA) evidence for this event

The strong hyperkahler SYZ conjecture evidence for this event

VibeMathed record: The strong hyperkahler SYZ conjecture evidence for this event

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