Open Access
October, 2011 A necessary condition for Chow semistability of polarized toric manifolds
Hajime ONO
J. Math. Soc. Japan 63(4): 1377-1389 (October, 2011). DOI: 10.2969/jmsj/06341377


Let $\Delta \subset R^n$ 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 $(C^\times)^n$-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.


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Hajime ONO. "A necessary condition for Chow semistability of polarized toric manifolds." J. Math. Soc. Japan 63 (4) 1377 - 1389, October, 2011.


Published: October, 2011
First available in Project Euclid: 27 October 2011

zbMATH: 1230.14069
MathSciNet: MR2855816
Digital Object Identifier: 10.2969/jmsj/06341377

Primary: 14L24
Secondary: 14M25 , 52B20

Keywords: Chow semistability , polarized toric manifold

Rights: Copyright © 2011 Mathematical Society of Japan

Vol.63 • No. 4 • October, 2011
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