Chow stability of λ-stable toric varieties

For a given polarized toric variety, we define the notion of λ-stability which is a natural generalization of uniform K-stability. At the neighbourhoods of the vertices of the corresponding moment polytope Δ, we consider appropriate triangulations and give a sufficient criteria for a λ-stable polarized toric variety $(X,L)$ to be asymptotically Chow polystable when the obstruction of asymptotic Chow semistability (the Futaki-Ono invariant) vanishes. As an application, we prove that any K-semistable polarized smooth toric variety $(X,L)$ with the vanishing Futaki-Ono invariant is asymptotically Chow polystable.