Proves the strong hyperkähler SYZ conjecture: every holomorphic line bundle with nonzero nef isotropic first Chern class on a compact irreducible holomorphic symplectic Kähler manifold is semiample. It also proves that every projective Lagrangian fibration with normal projective base has projective space as its base, in every dimension and deformation type.
Manuscripts (2)
Projective-space bases of Lagrangian fibrations
September 23, 2026 · source · cite as \cite{OAI:Projective-Space-Bases-of-Lagrangian-Fibrations-September-23-2026}
We prove that the normal projective base of a projective Lagrangian fibration from a compact irreducible holomorphic symplectic Kähler manifold is projective space. This resolves the projective-space base conjecture for such fibrations in every dimension and deformation type.
The strong hyperkähler SYZ conjecture
September 23, 2026 · source · cite as \cite{OAI:The-Strong-Hyperkahler-SYZ-Conjecture-September-23-2026}
We prove the strong hyperkähler SYZ conjecture: every holomorphic line bundle with nonzero nef isotropic first Chern class on a compact irreducible holomorphic symplectic Kähler manifold is semiample.
Result 041 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md