Algebraic and complex geometry·OpenAI Math·Result 051
Kobayashi’s canonical-ampleness conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under algebraic and complex geometry: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
Canonical ampleness of compact hyperbolic Kähler manifolds
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What OpenAI claims
Every compact connected Kähler manifold of positive complex dimension with no nonconstant entire curve has ample canonical bundle and is therefore projective. This proves Kobayashi's canonical-ampleness conjecture in the smooth compact Kähler setting.
Paper
Canonical ampleness of compact hyperbolic Kähler manifolds
We prove that every compact connected Kähler manifold of positive complex dimension containing no nonconstant entire curve has ample canonical bundle and is projective. This resolves positively Kobayashi's canonical-ampleness conjecture in the smooth compact Kähler category.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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