Normal del Pezzo surfaces containing a nonrational singularity

2000/01/31 by Stefan Schroeer
Mathematics · #math.AG #msc:14J17 #msc:14J20 #msc:14J25 #msc:14J26

paper · pdf

published as Manuscr. Math. 104 (2001), 257-274. · Minor changes, 17 pages, to appear in Manuscr. Math

arxiv created 2001/05/07 · arxiv updated 2009/11/30

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.

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