On the classification of singular cubic threefolds

2023/04/20 by Sasha Viktorova, Viktorova, Sasha
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2304.10452

openalex publication_date 2023/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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