2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58556Working over a perfect field, I classify normal del Pezzo surfaces with base number one that contain a nonrational singularity. They form a huge infinite hierarchy; contractions of ruled surfaces lie on top of it. Descending the hierarchy hinges on a generalized version of elementary transformations. As an application, I determine the structure of 2-dimensional anticanonical models for arbitrary normal surfaces.Minor changes, 17 pages, to appear in Manuscr. MathAlgebraic Geometry14J17, 14J20, 14J25, 14J26text