Work

Asymptotic Chow stability of symmetric reflexive toric varieties

Year: 2025

Type: article

Abstract: In this note, we study the asymptotic Chow stability of symmetric reflexive toric varieties. We provide examples of symmetric reflexive toric varieties that are not asymptotically Chow semistable. On the other hand, we also show that any weakly symmetric reflexive toric varieties which have a regular triangulation (so are special) are asymptotically Chow polystable. Furthermore, we give sufficient criteria to determine when a toric variety is asymptotically Chow polystable. In particular, two examples of toric varieties are given that are asymptotically Chow polystable, but not special. We also provide some examples of special polytopes, mainly in two or three dimensions, and some in higher dimensions.

Source: Moduli

DOI: 10.1112/mod.2025.1

Author: King Leung Lee

Institutions: Université de Montpellier, Institut Montpelliérain Alexander Grothendieck

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,450

Funders: Instituto de Ciencias Matemáticas, European Commission, Universidad Autónoma de Madrid, NextGenerationEU