The generalized Mukai conjecture
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 \(\mathbb P^{\iota-1}\).
Cite
@misc{OAI:The-Generalized-Mukai-Conjecture-September-24-2026,
author = {{OpenAI}},
title = {{The generalized Mukai conjecture}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/The-Generalized-Mukai-Conjecture-September-24-2026/article.pdf}{OAI:The-Generalized-Mukai-Conjecture-September-24-2026}},
year = {2026}
}