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arXiv · 2009.02271

On toric geometry and K-stability of Fano varieties

Anne-Sophie Kaloghiros·Andrea Petracci
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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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Anne-Sophie Kaloghiros, Andrea Petracci. 2021-05-03. On toric geometry and K-stability of Fano varieties. https://doi.org/10.1090/btran%2F82

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