English

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.

Keywords

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