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On the classification of singular cubic threefolds

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arxiv 2304.10452 v2 pith:HISCEJSU submitted 2023-04-20 math.AG

Sasha Viktorova This is my paper · ORCID
classification math.AG
keywords cubicsingularitiesthreefoldsadditionanalogousbruce--wallcertainclassification
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We classify combinations of isolated singularities that can occur on complex cubic threefolds generalizing analogous results for cubic surfaces due to Schl\"{a}fli 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.

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  1. Equivariant geometry of cubic threefolds with non-isolated singularities

    math.AG 2025-05 conditional novelty 7.0 of 10

    Every finite group action on a cubic threefold singular along a line, plane, or the chordal curve is linearizable; actions on cubics singular along a conic are generally not linearizable, though all such actions are u...

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