OpenAI research collection · 1 manuscript · Source checked 2026-10-19
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)≤ n, with equality exactly for (\mathbb P^{\iota-1})^\rho. Here the pseudoindex is the least anticanonical degree of a rational curve.
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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)≤ n. Equality holds precisely for the product of ρ copies of \mathbb P^{\iota-1}.
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