Proves the generalized Mukai conjecture: every positive-dimensional smooth complex projective Fano manifold of dimension n, Picard number ρ and pseudoindex ι satisfies \rho(\iota-1)\le n, with equality exactly for (\mathbb P^{\iota-1})^\rho. Here the pseudoindex is the least anticanonical degree of a rational curve.
Manuscript
The generalized Mukai conjecture
September 24, 2026 · source · cite as \cite{OAI:The-Generalized-Mukai-Conjecture-September-24-2026}
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}.
Result 063 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md