{"id":"openai-math/The-Campana-Peternell-conjecture-in-dimension-six","pdf":"https://github.com/openai/math/blob/main/preprints/The-Campana-Peternell-conjecture-in-dimension-six-September-25-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Campana-Peternell-conjecture-in-dimension-six-September-25-2026","tags":["complex-geometry","fano-varieties","nef-tangent-bundle"],"score":0,"title":"The Campana–Peternell conjecture in dimension six","domain":"Algebraic and complex geometry","family":"067","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"The Campana–Peternell conjecture in dimension six"}