Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 53, Number 3 (2016), 751-765.
Facets of secondary polytopes and chow stability of toric varieties
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 . 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.
Osaka J. Math., Volume 53, Number 3 (2016), 751-765.
First available in Project Euclid: 5 August 2016
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Yotsutani, Naoto. Facets of secondary polytopes and chow stability of toric varieties. Osaka J. Math. 53 (2016), no. 3, 751--765. https://projecteuclid.org/euclid.ojm/1470413988