CATALOGUE 067
The Campana–Peternell conjecture in dimension six
This catalogue contains one manuscript. It treats complex dimension six of the general Campana–Peternell conjecture, combining known Picard-number and pseudoindex cases with characteristic-number constraints from two fibrations and VMRT recognition. It also derives a statement about ordinary universal covers of compact Kähler manifolds whose Albanese-fibre dimension is at most six.
1. Papers in official order
These summaries give the principal scope; consult the cited original results for the complete hypotheses and statements.
Page counts include references. On narrow screens, scroll the table sideways.
| # | Manuscript and overview | Principal claim | Role and available overview |
|---|---|---|---|
| 01 | The Campana–Peternell conjecture in dimension six →Short name: The Campana–Peternell conjecture in dimension sixSeptember 25, 2026 · 27 pagesOriginal paper (GitHub) ↗ | Rational homogeneity of Fano sixfolds with nef tangent bundle; consequences for universal covers with Albanese-fibre dimension at most six and positive Kähler–Einstein metrics. Theorem 1.1 · p. 2; Corollary 1.2 · p. 4; Corollary 7.1 · p. 21 ↗ | Combines known Picard-number and pseudoindex cases with characteristic-number constraints from two fibrations and VMRT recognition. Read the proof overview → |
2. Where to begin
The article's overview diagram separates the known $\rho\ge2$ branch from pseudoindices four and five at $\rho=1$. The numerical constraint and VMRT recognition form the central argument. The Albanese corollary distinguishes the bundle on a finite cover from the product on the universal cover.
The inputs come from established literature outside the catalogue. No direct citation to another OpenAI manuscript was found in the manuscript's text and bibliography. Further inclusion or generalization relations with other catalogues remain uninvestigated.
3. Sources and checking scope
The official number and title were checked against p.8 of the fixed OpenAI Research Catalog overview PDF, and the manuscript order against the corresponding CONTENTS file. The manuscript is dated 25 September 2026 and has 27 pages including references.
OpenAI Research Catalog · Catalogue 067 · p. 8 Theorem 1.1; Corollary 1.2 · pp. 2–4
The principal results and proof connections, and the statements and applications of known inputs, received an editorial self-check. This is neither independent peer review nor formal verification of complete proofs. See the article's closing section for source-specific checks and unresolved items.