Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 067-01. The Campana–Peternell conjecture in dimension six
Manuscript map · lines 3795–3804
OpenAI@2026-10-07#rem:oai-p-067-01
Authors: OpenAI. Family 067.
Title: The Campana–Peternell conjecture in dimension six.
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 $F{}times{}mathbb C{}{{}widetilde q(X)}$, where F is a rational homogeneous manifold and ${}widetilde q(X)$ is the maximal irregularity of a connected finite étale cover.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- section: Manuscript map
- remark: Remark: 001-01. Milne's rationality conjecture for abelian varieties
- remark: Remark: 002-01. Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank
- remark: Remark: 002-02. The Selmer converse for elliptic curves at every prime
- remark: Remark: 002-03. The two-primary Birch–Swinnerton-Dyer formula in Selmer corank at most one
- remark: Remark: 003-01. The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane s 7/8
- remark: Remark: 003-02. The Quasi-Riemann Hypothesis (alternate 11/12 proof)
- remark: Remark: 003-03. Uniform exclusion of Landau–Siegel zeros