The projective-space base conjecture for Lagrangian fibrations of compact hyperkahler manifolds

Theorem 1.1: if $f:X\to B$ is a projective surjective connected-fibre morphism from a compact IHS Kahler manifold of dimension $2n$ onto a normal projective $n$ -dimensional $B$ , with every fibre component $n$ -dimensional and isotropic for $\sigma$ , then $B\cong\mathbb P^n$ , with no smoothness assumption on $B$ , no bound on $b_2$ and no restriction on deformation type. With Kim-Oguiso-Shinder it excludes codimension-one multiple fibres. Not shown: the case of a nonprojective $X$ (Kahler $X$ with a non-projective morphism).

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Prior state unknown→proved

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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 projective-space base conjecture for Lagrangian fibrations of compact hyperkahler manifolds · Base of a Lagrangian fibration is P^n

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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VibeMathed record: The projective-space base conjecture for Lagrangian fibrations of compact hyperkahler manifolds

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 of 'Projective-space bases of Lagrangian fibrations' and its introduction were read against the conjecture as the paper states it. The proof (local cotangent tensors and a Deligne-Mumford stratum, an Euler-characteristic obstruction via reduction to positive characteristic, a second Lagrangian fibration from deformations, then Hwang's theorem) was not refereed. No Lean formalization. It depends on the unreviewed SYZ companion. Scope the paper itself states: projective fibrations (relatively ample bundle) onto a normal projective base with equidimensional Lagrangian fibres, so X is projective; the nonprojective Kahler case of the conjecture is not claimed.

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Same family: Projective-space bases of Lagrangian fibrations

paper · pending

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The strong hyperkahler SYZ conjecture

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VibeMathed record: The projective-space base conjecture for Lagrangian fibrations of compact hyperkahler manifolds evidence for this event

The strong hyperkahler SYZ conjecture evidence for this event

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