Non-symplectic Indices of Automorphism Groups of Smooth Cubic Fourfolds

@misc{fu2026nonsymplectic,
  title = {{Non-symplectic Indices of Automorphism Groups of Smooth Cubic Fourfolds}},
  author = {Jie Fu and Shihao Wang and Zhiwei Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.11754},
  eprint = {2606.11754},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.11754},
}

TY  - UNPB
TI  - Non-symplectic Indices of Automorphism Groups of Smooth Cubic Fourfolds
AU  - Jie Fu
AU  - Shihao Wang
AU  - Zhiwei Zheng
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2606.11754
UR  - https://arxiv.org/abs/2606.11754
AB  - We study the full automorphism groups of smooth cubic fourfolds with prescribed symplectic automorphism group. Our starting point is the classification of symplectic automorphism groups by Laza and Zheng. We focus on the non-symplectic index, namely, the index of the symplectic automorphism group in the full automorphism group. We prove general restrictions on this index. We also compute bounds by group-theoretic and lattice-theoretic methods. In several cases, we determine all possible indices. For coinvariant lattices of rank 19, we classify all possible pairs consisting of the symplectic automorphism group and the full automorphism group.
ER  -