Degenerations of Jordan algebras

@misc{bovdi2026degenerations,
  title = {{Degenerations of Jordan algebras}},
  author = {Victor Bovdi and Ivan Kaygorodov and Yury Popov and Azamat Saydaliyev and Yury Volkov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31179},
  eprint = {2610.31179},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31179},
}

TY  - UNPB
TI  - Degenerations of Jordan algebras
AU  - Victor Bovdi
AU  - Ivan Kaygorodov
AU  - Yury Popov
AU  - Azamat Saydaliyev
AU  - Yury Volkov
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31179
UR  - https://arxiv.org/abs/2610.31179
AB  - We describe all degenerations of complex $4$-dimensional Jordan algebras and of complex $5$-dimensional nilpotent Jordan algebras. The proofs do not use other papers on degenerations, and all degenerations and non-degenerations were formally verified in the proof assistant Lean~4. The graph of primary degenerations of $4$-dimensional Jordan algebras has $73$ vertices and $160$ edges. The variety of $5$-dimensional nilpotent Jordan algebras is stratified into $63$ normal forms, five of which are one- or two-parameter families; together with two special members of a family this gives $65$ objects, and the graph of primary degenerations has $154$ edges. In particular, we describe all irreducible components of the corresponding varieties: the variety of $4$-dimensional Jordan algebras has $10$ irreducible components, and the variety of $5$-dimensional nilpotent Jordan algebras has dimension $22$ and $5$ irreducible components.
ER  -