Publications of the Research Institute for Mathematical Sciences
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Nonnormal del Pezzo Surfaces
Miles Reid (1)(1) Mathematics Institute, University of Warwick, CV4 7AL, COVENTRY, UNITED KINGDOM
This paper studies reduced, connected, Gorenstein surfaces with ample-K, assumed to be reducible or nonnormal. The normalisation is a union of one or more standard surfaces (scrolls and Veronese surfaces), marked with a conic as double locus. The question is how to glue these together to get a Gorenstein scheme. In characteristic 0, the results amount to a classification of projective surfaces in the style of the 1880s. However, the methods involve a study of the dualising sheaf of a nonnormal variety in terms of Rosenlicht differentials, and there is a subtle pathology in characteristic p due to Mori and S. Goto.