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July 2016 Facets of secondary polytopes and chow stability of toric varieties
Naoto Yotsutani
Osaka J. Math. 53(3): 751-765 (July 2016).


Chow stability is one notion of Mumford's geometric invariant theory for studying the moduli space of polarized varieties. Kapranov, Sturmfels and Zelevinsky detected that Chow stability of polarized toric varieties is determined by its inherent secondary polytope, which is a polytope whose vertices correspond to regular triangulations of the associated polytope [7]. In this paper, we give a purely convex-geometrical proof that the Chow form of a projective toric variety is $H$-semistable if and only if it is $H$-polystable with respect to the standard complex torus action $H$. This essentially means that Chow semistability is equivalent to Chow polystability for any (not-necessaliry-smooth) projective toric varieties.


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Naoto Yotsutani. "Facets of secondary polytopes and chow stability of toric varieties." Osaka J. Math. 53 (3) 751 - 765, July 2016.


Published: July 2016
First available in Project Euclid: 5 August 2016

zbMATH: 06629523
MathSciNet: MR3533467

Primary: 51M20
Secondary: 53C55

Rights: Copyright © 2016 Osaka University and Osaka City University, Departments of Mathematics


Vol.53 • No. 3 • July 2016
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