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Mathematics > Algebraic Geometry

arXiv:2212.05000 (math)
[Submitted on 9 Dec 2022 (v1), last revised 18 Dec 2023 (this version, v4)]

Title:Asymptotic Chow stability of symmetric reflexive toric varieties

Authors:King Leung Lee
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Abstract:In this note, we study the asymptotic Chow stability of toric varieties. We provide examples of symmetric reflexive toric varieties that are not asymptotic Chow semistable. On the other hand, we also show that any weakly symmetric reflexive toric varieties which have regular triangulation (special) are asymptotic Chow polystable.
After that, we provide another criteria that can show a symmetric reflexive toric variety is asymptotic Chow polystable. In particular, we give two examples that are asymptotic Chow polystable, but not special. We also provide some examples of special polytopes, mainly in 2 or 3 dimensions, and some in higher dimensions.
Comments: 21 pages, 6 figures. Rename the title aback to the first version. Also, rename the Chow Futaki invariant as Futaki-Ono invariant
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14J15, 14M25, 52B99
Cite as: arXiv:2212.05000 [math.AG]
  (or arXiv:2212.05000v4 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2212.05000

Submission history

From: King Leung Lee [view email]
[v1] Fri, 9 Dec 2022 17:36:48 UTC (27 KB)
[v2] Tue, 13 Dec 2022 08:59:05 UTC (26 KB)
[v3] Thu, 30 Nov 2023 16:17:39 UTC (26 KB)
[v4] Mon, 18 Dec 2023 17:12:38 UTC (26 KB)
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