K-stability of Fano threefolds of rank 3 and degree 14

Grigory Belousov; Konstantin Loginov

K-stability of Fano threefolds of rank 3 and degree 14

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arxiv 2403.03700 v3 pith:EJXMBLQZ submitted 2024-03-06 math.AG

Grigory Belousov , Konstantin Loginov This is my paper · ORCID

classification math.AG

keywords degreefanorankthreefoldsconditionexplicitlygeneralgenerality

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abstract

We prove that all general smooth Fano threefolds of Picard rank $3$ and degree $14$ are K-stable, where the generality condition is stated explicitly.

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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.

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