Source: J. Math. Soc. Japan
Volume 63, Number 4
Let Δ ⊂ Rn be an n-dimensional Delzant polytope. It is well-known that there exist the n-dimensional compact toric manifold XΔ and the very ample (C×)n-equivariant line bundle LΔ on XΔ associated with Δ. In the present paper, we show that if (XΔ, LΔi) is Chow semistable then the sum of integer points in iΔ is the constant multiple of the barycenter of Δ. Using this result we get a necessary condition for the polarized toric manifold (XΔ, LΔ) being asymptotically Chow semistable. Moreover we can generalize the result in  to the case when XΔ is not necessarily Fano.
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