2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68706Let X be a Fano variety of dimension n, pseudoindex i_X and Picard number ρ_X. A generalization of a conjecture of Mukai says that ρ_X(i_X-1)\le n. We prove that the conjecture holds if: a) X has pseudoindex i_X \ge \frac{n+3}{3} and either has a fiber type extremal contraction or does not have small extremal contractions b) X has dimension five.19 pagesAlgebraic Geometry14J45, 14E30text