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PreprintarXiv licencearXiv

Automorphism Groups of Smooth Cubic Fourfolds through Lattice Theory

  • Jie Fu
  • Zhiwei Zheng
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Abstract

Laza and the second author have classified all possible symplectic automorphism groups of smooth cubic fourfolds. There are $34$ such groups, and by Koike, there are $48$ families of cubic fourfolds with speficied symplectic automorphism group. For $42$ among those families, we complete the classification of all possible automorphism groups. The approach of this paper is mainly lattice theoretic, starting from known results about the period map of cubic fourfolds by Voisin, Hassett, Looijenga and Laza. We use a lattice-enumeration algorithm implemented in OSCAR.

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Cite

BibTeXRIS
BibTeX
@misc{fu2026automorphism,
  title = {{Automorphism Groups of Smooth Cubic Fourfolds through Lattice Theory}},
  author = {Jie Fu and Zhiwei Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06683},
  eprint = {2609.06683},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06683},
}
RIS
TY  - UNPB
TI  - Automorphism Groups of Smooth Cubic Fourfolds through Lattice Theory
AU  - Jie Fu
AU  - Zhiwei Zheng
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06683
UR  - https://arxiv.org/abs/2609.06683
AB  - Laza and the second author have classified all possible symplectic automorphism groups of smooth cubic fourfolds. There are $34$ such groups, and by Koike, there are $48$ families of cubic fourfolds with speficied symplectic automorphism group. For $42$ among those families, we complete the classification of all possible automorphism groups. The approach of this paper is mainly lattice theoretic, starting from known results about the period map of cubic fourfolds by Voisin, Hassett, Looijenga and Laza. We use a lattice-enumeration algorithm implemented in OSCAR.
ER  -