{"id":"openai-math/Projective-Space-Bases-of-Lagrangian-Fibrations","pdf":"https://github.com/openai/math/blob/main/preprints/Projective-Space-Bases-of-Lagrangian-Fibrations-September-23-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Projective-Space-Bases-of-Lagrangian-Fibrations-September-23-2026","tags":["algebraic-geometry","lagrangian-fibrations","hyperkahler-manifolds","complex-geometry"],"score":0,"title":"Projective-space bases of Lagrangian fibrations","domain":"Algebraic and complex geometry","family":"041","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Hyperkähler SYZ and projective-space bases"}