The Campana–Peternell conjecture in dimension six

What OpenAI claims

Proves the Campana–Peternell conjecture in complex dimension six: every smooth connected complex projective Fano sixfold with nef tangent bundle is rational homogeneous.

Paper

1. The Campana–Peternell conjecture in dimension six

   25 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract We prove that every smooth connected complex projective Fano sixfold with nef tangent bundle is rational homogeneous, resolving the Campana–Peternell conjecture in complex dimension six. As a consequence, a connected compact Kähler manifold X with nef holomorphic tangent bundle and dim_ℂX-q̃(X) ≤ 6 has ordinary universal cover F×ℂ^q̃(X), where F is a rational homogeneous manifold and q̃(X) is the maximal irregularity of a connected finite étale cover.

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.