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.