OpenAI research collection · 1 manuscript · Source checked 2026-10-19
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Proves the Campana–Peternell conjecture in complex dimension six: every smooth connected complex projective Fano sixfold with nef tangent bundle is rational homogeneous.
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MANUSCRIPT 01
The Campana–Peternell conjecture in dimension six
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…
Full source 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_{\mathbb C}X-\widetilde q(X)\leq6 has ordinary universal cover F×\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.
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