2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147073In the present paper we discuss coherent sheaves of rank > 1 whose projectivization gives rise to smooth varieties - varieties of this type are also called smooth scrolls. We prove some basic properties of these varieties and we give some pertinent examples. We classify Fano manifolds of large index which are of this type.19 pages, plain TeXAlgebraic Geometrytext