English

On the classification of singular cubic threefolds

Algebraic Geometry 2024-05-07 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2304.10452,
  title  = {On the classification of singular cubic threefolds},
  author = {Sasha Viktorova},
  journal= {arXiv preprint arXiv:2304.10452},
  year   = {2024}
}

Comments

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

R2 v1 2026-06-28T10:12:43.999Z