A necessary condition for Chow semistability of polarized toric manifolds

作者：Ono Hajime^*

来源：Journal of the Mathematical Society of Japan, 2011, 63(4): 1377-1389.

DOI：10.2969/jmsj/06341377

• Chow semistability
• polarized toric manifold

Let Delta subset of R-n be an n-dimensional Delzant polytope. It is well-known that there exist the n-dimensional compact toric manifold X-Delta and the very ample (Cx)n-equivariant line bundle L-Delta on X-Delta associated with Delta. In the present paper, we show that if (X-Delta, L-Delta(i)) is Chow semistable then the sum of integer points in i Delta is the constant. multiple of the barycenter of Delta. Using this result we get a necessary condition for the polarized toric manifold (X-Delta, L-Delta) being asymptotically Chow semistable. Moreover we can generalize the result in [4] to the case when X-Delta is not necessarily Fano.

• 出版日期2011-10