The Campana–Peternell conjecture in dimension six

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

Manuscript

The Campana–Peternell conjecture in dimension six

September 25, 2026 · source · cite as \cite{OAI:The-Campana-Peternell-conjecture-in-dimension-six-September-25-2026}

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_{\mathbb C}X-\widetilde q(X)\leq6 has ordinary universal cover F\times\mathbb C^{\widetilde q(X)}, where F is a rational homogeneous manifold and \widetilde q(X) is the maximal irregularity of a connected finite étale cover.

Result 067 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.