On toric geometry and K-stability of Fano varieties

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.

arXiv comment29 pages. v2: minor revision

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Cited by in corpus (4)

• On K-stability of some del Pezzo surfaces of Fano index 2
• On deformation spaces of toric singularities and on singularities of K-moduli of Fano varieties
• K-moduli of Fano 3-folds can have embedded points
• Foldable fans, cscK surfaces and local K-moduli