K-stable Fano 3-folds in the families 2.18 and 3.4

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arxiv 2304.11334 v1 pith:SSMG257N submitted 2023-04-22 math.AG

Ivan Cheltsov , Kento Fujita , Takashi Kishimoto , Jihun Park This is my paper · ORCID

classification math.AG

keywords familiesfanofoldsk-stableprovesmooth

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We prove that smooth Fano 3-folds in the families 2.18 and 3.4 are K-stable.

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K-stability of Fano 3-folds in the World of Null-A
math.AG 2025-05 accept novelty 6.0 of 10

Every smooth Fano 3-fold that fails Condition (A), meaning it has a finite abelian automorphism group with no fixed point, is K-polystable except for eight explicit deformation families.