Nonnormal del Pezzo surfaces

Details Nonnormal del Pezzo surfaces Nonnormal del Pezzo surfaces

1994-04-05

arxiv.org/abs/alg-geom/9404002v1

Mathematics

Algebraic Geometry

amsTeX 2.1 (amsppt format), submitted to Math Proceedings, RIMS

Scientific paper

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.

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