OpenAI reports the Campana–Peternell conjecture for Fano sixfolds

Every smooth connected complex projective Fano variety of dimension six with nef tangent bundle is rational homogeneous.

Sources for this record

What was already known

The Campana–Peternell conjecture was established in dimensions at most five. In dimension six, a prior Picard-number bound covered every case with Picard number at least two, leaving the Picard-number-one case (manuscript introduction, p. 2).

AI involvement AI-led

OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.

OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.

Importance Notable

Completes the Campana–Peternell classification in complex dimension six.

Limitations

The result is restricted to smooth projective Fano sixfolds with nef tangent bundle; the general conjecture in higher dimensions remains.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.

Correction and publication history

2026-10-18 · publication

Primary manuscript, attribution, and prior-work review for non-notifying local inclusion.

Read this published revision