For toric rational curves with one unibranch singularity, the worst destabilizing one-parameter subgroup is eventually constant on an initial segment and linear on the tail, with explicit formulas.
Jensen, Gfan, a software system for Gr¨ obner fans and tropical varie ties
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The worst destabilizing 1-parameter subgroup for toric rational curves with one unibranch singularity
For toric rational curves with one unibranch singularity, the worst destabilizing one-parameter subgroup is eventually constant on an initial segment and linear on the tail, with explicit formulas.