On toric geometry and K-stability of Fano varieties
Algebraic Geometry
2021-09-02 v2
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.
Cite
@article{arxiv.2009.02271,
title = {On toric geometry and K-stability of Fano varieties},
author = {Anne-Sophie Kaloghiros and Andrea Petracci},
journal= {arXiv preprint arXiv:2009.02271},
year = {2021}
}
Comments
29 pages. v2: minor revision