{"id":"openai-math/The-Generalized-Mukai-Conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/The-Generalized-Mukai-Conjecture-September-24-2026/article.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Generalized-Mukai-Conjecture-September-24-2026","tags":["algebraic-geometry","fano-manifolds","pseudoindex","picard-number"],"score":0,"title":"The generalized Mukai conjecture","domain":"Algebraic and complex geometry","family":"063","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove the generalized Mukai conjecture: every positive-dimensional smooth complex Fano manifold of dimension n , Picard number ρ , and pseudoindex ι satisfies $`\\rho(\\iota-1)\\le n`$. Equality holds precisely for the product of ρ copies of $`\\mathbb P^{\\iota-1}`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://x.com/ivanswzhang/status/2110157177126260925","date":"2026-10-13","kind":"x","added":"2026-10-24","author":"Shaowu Zhang","handle":"ivanswzhang"}],"formalized":false,"family_title":"The generalized Mukai conjecture"}