2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107747We give the first evidence for a conjecture that a general, index-one, Fano hypersurface is not unirational: (i) a general point of the hypersurface is contained in no rational surface ruled, roughly, by low-degree rational curves, and (ii) a general point is contained in no image of a Del Pezzo surface.13 pages, 6 diagramsAlgebraic Geometry14C05; 14E08text