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Analysis identifies singularity combinations in cubic threefolds, suggesting new graph configurations.
We classify combinations of isolated singularities that can occur on complex cubic threefolds generalizing analogous results for cubic surfaces (see Schläfli [Philos. Trans. Roy. Soc. 153 (1863), pp. 193–241] and Bruce and Wall [J. London Math. Soc. (2) 19 (1979), pp. 245–256]). In addition, we provide concise combinatorial description of the possible configurations of simple singularities: they essentially correspond to subgraphs of a certain graph.
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Sasha Viktorova (2025) studied this question.
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