On the classification of singular cubic threefolds

Abstract

We classify combinations of isolated singularities that can occur on complex cubic threefolds generalizing analogous results for cubic surfaces due to Schläfli and Bruce--Wall. In addition, we provide concise combinatorial description of the possible configurations of simple singularities: they essentially correspond to subgraphs of a certain graph.

28 pages, 10 figures, 9 tables; comments welcome! v2: corrected typos, minor edits, added Def. 1.12