Normal del Pezzo surfaces containing a nonrational singularity

Details Normal del Pezzo surfaces containing a nonrational singularity Normal del Pezzo surfaces containing a nonrational singularity

2000-01-22

arxiv.org/abs/math/0001118v2

Manuscr. Math. 104 (2001), 257-274.

Mathematics

Algebraic Geometry

Minor changes, 17 pages, to appear in Manuscr. Math

Scientific paper

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.

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