2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110048We study Gorenstein almost Fano threefolds X with canonical singularities and pseudoindex > 1. We show that the maximal Picard number of X is 10 in general, 3 if X is Fano, and 8 if X is toric. Moreover, we characterize the boundary cases. In the Fano case, we prove that the generalized Mukai conjecture holds.18 pagesAlgebraic Geometry14J30, 14J45, 14E30, 14M25text