On toric geometry and K-stability of Fano varieties

Kaloghiros, Anne-Sophie; Petracci, Andrea

doi:10.1090/btran/82

On toric geometry and K-stability of Fano varieties
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by Anne-Sophie Kaloghiros and Andrea Petracci HTML | PDF

Trans. Amer. Math. Soc. Ser. B 8 (2021), 548-577

Abstract:

We present some applications of the deformation theory of toric Fano varieties to K-(semi/poly)stability of Fano varieties. First, we present two examples of K-polystable toric Fano $3$-fold with obstructed deformations. In one case, the K-moduli spaces and stacks are reducible near the closed point associated to the toric Fano $3$-fold, while in the other they are non-reduced near the closed point associated to the toric Fano $3$-fold. Second, we study K-stability of the general members of two deformation families of smooth Fano $3$-folds by building degenerations to K-polystable toric Fano $3$-folds.

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