The generalized Mukai conjecture. 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.
released 2026-09-24 | 3 theorems · 6 lemmas · 10 proofs · 7,794 words |
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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 $\mathbb P^{\iota-1}$.