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November 2013 Algebro-geometric semistability of polarized toric manifolds
Hajime Ono
Asian J. Math. 17(4): 609-616 (November 2013).


Let $\Delta \subset \mathbb{R}^n$ be an $n$-dimensional integral Delzant polytope. It is well-known that there exist the $n$-dimensional compact toric manifold $X_{\Delta}$ and a very ample $(\mathbb{C}×)^n$-equivariant line bundle $L_{\Delta}$ on $X_{\Delta}$ associated with $\Delta$. In the present paper, we give a necessary and sufficient condition for Chow semistability of $( X_{\Delta}, {L^i}_{\Delta})$ for a maximal torus action. We then see that asymptotic (relative) Chow semistability implies (relative) K-semistability for toric degenerations, which is proved by Ross and Thomas.


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Hajime Ono. "Algebro-geometric semistability of polarized toric manifolds." Asian J. Math. 17 (4) 609 - 616, November 2013.


Published: November 2013
First available in Project Euclid: 22 August 2014

zbMATH: 1297.14056
MathSciNet: MR3152255

Primary: 14L24 , 14M25 , 52B20

Keywords: Chow stability , K-stability , polarized toric manifold

Rights: Copyright © 2013 International Press of Boston

Vol.17 • No. 4 • November 2013
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