OpenAI · 063-01 · 2026-09-24 · Algebraic and complex geometry

The generalized Mukai conjecture

preprints/The-Generalized-Mukai-Conjecture-September-24-2026

Family 063. The generalized Mukai conjecture.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N

Proves the generalized Mukai conjecture: every positive-dimensional smooth complex projective Fano manifold of dimension $n$ , Picard number $ρ$ and pseudoindex $ι$ satisfies $ρ (ι - 1) \leq n$ , with equality exactly for $(P^{ι - 1})^{ρ}$ . Here the pseudoindex is the least anticanonical degree of a rational curve.

We prove the generalized Mukai conjecture: every positive-dimensional smooth complex Fano manifold of dimension n, Picard number ρ, and pseudoindex ι satisfies $ρ (ι - 1) \leq n$ . Equality holds precisely for the product of ρ copies of $P^{ι - 1}$ .

Preprint source and Lean scope

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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.