Year: 2026
Type: preprint
Abstract: For K-unstable toric varieties, Székelyhidi's optimal test-function $Θ_{P}$ is a mysterious concave function over the moment polytope $P$, which gives the maximal destabilizer for K-stability, and encodes the limiting behavior of the divergent Calabi flow. As balanced norms quantize cscK metrics, we show that $Θ_{P}$ can be quantized by the maximal destabilizers for Chow-stability, which are given by the shortest GKZ vectors, i.e., the least norm point on the secondary polytope for the set $P\cap k^{-1}\mathbb{Z}^{n}$. Properties and algorithm for general sGKZ vectors are given. Our result may provide a new method to detect the K-unstability of toric varieties.
Source: arXiv (Cornell University)
Authors: Li, Chi, Sheng, Li, Yao, Yi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220721199