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Peer-reviewedCC BYTransformation groups

K-stability of Fano 3-folds in the World of Null-A.

  • Hamid Abban1
  • Ivan Cheltsov2
  • Takashi Kishimoto3
  • Frédéric Mangolte4
4 affiliations
  1. 1University of Nottingham, Nottingham, England.
  2. 2University of Edinburgh, Edinburgh, Scotland.
  3. 3Saitama University, Saitama, Japan.
  4. 4Aix Marseille University, CNRS, I2M, Marseille, France.
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Abstract

A variety is said to satisfy Condition (A) if every finite abelian subgroup of its automorphism group has a fixed point. We show that a smooth Fano 3-fold not satisfying Condition (A) is K-polystable unless it is contained in eight exceptional deformation families (seven of them consist of one smooth member, and one of them has two-parameter moduli).

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Cite

BibTeXRIS
BibTeX
@article{abban2026kstability,
  title = {{K-stability of Fano 3-folds in the World of Null-A.}},
  author = {Hamid Abban and Ivan Cheltsov and Takashi Kishimoto and Frédéric Mangolte},
  journal = {Transformation groups},
  year = {2026},
  month = jul,
  doi = {10.1007/s00031-026-09977-9},
  url = {https://europepmc.org/article/MED/42996768},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - K-stability of Fano 3-folds in the World of Null-A.
AU  - Hamid Abban
AU  - Ivan Cheltsov
AU  - Takashi Kishimoto
AU  - Frédéric Mangolte
PY  - 2026
DA  - 2026/07/08
JO  - Transformation groups
DO  - 10.1007/s00031-026-09977-9
UR  - https://europepmc.org/article/MED/42996768
AB  - A variety is said to satisfy Condition (A) if every finite abelian subgroup of its automorphism group has a fixed point. We show that a smooth Fano 3-fold not satisfying Condition (A) is K-polystable unless it is contained in eight exceptional deformation families (seven of them consist of one smooth member, and one of them has two-parameter moduli).
SN  - 1531-586X
ER  -