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.
Cite this article
Miles Reid, Nonnormal del Pezzo Surfaces. Publ. Res. Inst. Math. Sci. 30 (1994), no. 5, pp. 695–727DOI 10.2977/PRIMS/1195165581