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.
K-stability and space sextic curves of genus three
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abstract
We study Fano threefolds that can be obtained by blowing up the three-dimensional projective space along a smooth curve of degree six and genus three. We produce many new K-stable examples of such threefolds, and we describe all finite groups that can act faithfully on them.
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K-stability of Fano 3-folds in the World of Null-A
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.