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

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arxiv 2505.04330 v1 pith:ZY2VGIZO submitted 2025-05-07 math.AG

Hamid Abban , Ivan Cheltsov , Takashi Kishimoto , Frederic Mangolte This is my paper · ORCID
classification math.AG
keywords conditionfanosmooththemabelianautomorphismconsistscontained
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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 consists of one smooth member, and one of them has one-parameter moduli).

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  1. On K-stability of Fano's last Fanos

    math.AG 2025-07 accept novelty 7.0 of 10

    A smooth Fano threefold of Family no.2.16 is K-stable if a chosen finite automorphism group fixes no k-rational point of the singular locus of its discriminant quartic.

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