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PreprintarXiv licencearXiv

Small-Subgroup Criteria for Liftability of Automorphism Groups of Smooth Hypersurfaces

  • Baiting Xie
  • Zhiwei Zheng
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Abstract

In this paper, building on our previous Sylow criteria, we establish small-subgroup criteria of liftability and F-liftability for the linear automorphism group G of smooth hypersurfaces X over algebraically closed field of characteristic zero. When dim X = p−2 for some odd prime p, we prove that (F-)liftability of any finite subgroup of G can be tested on its p-subgroups of order at most p2. When X is a degree p hypersurface of dimension 2p−2, we prove that (F-)liftability of G can be tested on all its p-subgroups of order at most p3, which is sharp for p≥5. When p=3, this bound improves to $9$, giving the corresponding criteria for smooth cubic fourfolds.

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Cite

BibTeXRIS
BibTeX
@misc{xie2026smallsubgroup,
  title = {{Small-Subgroup Criteria for Liftability of Automorphism Groups of Smooth Hypersurfaces}},
  author = {Baiting Xie and Zhiwei Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15613},
  eprint = {2609.15613},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15613},
}
RIS
TY  - UNPB
TI  - Small-Subgroup Criteria for Liftability of Automorphism Groups of Smooth Hypersurfaces
AU  - Baiting Xie
AU  - Zhiwei Zheng
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15613
UR  - https://arxiv.org/abs/2609.15613
AB  - In this paper, building on our previous Sylow criteria, we establish small-subgroup criteria of liftability and F-liftability for the linear automorphism group G of smooth hypersurfaces X over algebraically closed field of characteristic zero. When dim X = p−2 for some odd prime p, we prove that (F-)liftability of any finite subgroup of G can be tested on its p-subgroups of order at most p^2. When X is a degree p hypersurface of dimension 2p−2, we prove that (F-)liftability of G can be tested on all its p-subgroups of order at most p^3, which is sharp for p≥5. When p=3, this bound improves to $9$, giving the corresponding criteria for smooth cubic fourfolds.
ER  -