Algebraic and complex geometry·OpenAI Math·Result 038
Fujita’s freeness 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
Fujita's freeness conjecture
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What OpenAI claims
Proves Fujita's freeness conjecture at its sharp bound in every dimension: for a smooth projective complex variety X of dimension n and an ample line bundle L, the adjoint KX+mL is globally generated for every integer m ≥ n+1.
Paper
Fujita's freeness conjecture
We prove Fujita's freeness conjecture. If X is a smooth complex projective variety of dimension n and L is an ample line bundle, then KX+mL is globally generated for every integer m ≥ n+1.
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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