Normal del Pezzo surfaces containing a nonrational singularity
arXiv:math/0001118
Abstract
Working 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. Math