Algebraic and complex geometry·OpenAI Math·Result 050·Lean formalisation listed
A counterexample to Griffiths’ positivity conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under algebraic and complex geometry: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
Ample rank-two bundles on the quadric surface without Griffiths-positive metrics
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What OpenAI claims
Constructs ample rank-two bundles on ℙ1×ℙ1 with no smooth Hermitian metric of strictly Griffiths-positive curvature, disproving Griffiths' positivity conjecture already on the quadric surface. (Lean)
Paper
Ample rank-two bundles on the quadric surface without Griffiths-positive metrics
We give counterexamples to Griffiths' conjecture in rank two on the quadric surface ℙ1×ℙ1. We construct an explicit bundle G whose coordinatewise power pullbacks, tensored with 𝒪(1,1), are ample for every positive power, but admit no smooth strictly Griffiths-positive Hermitian metric for all sufficiently large powers.
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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