Chow stability of $λ$-stable toric varieties
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916245366898688 |
|---|---|
| author | Lee, King leung Yotsutani, Naoto |
| author_facet | Lee, King leung Yotsutani, Naoto |
| contents | For a given polarized toric variety, we define the notion of $λ$-stability which is a natural generalization of uniform K-stability. At the neighbourhoods of the vertices of the corresponding moment polytope $Δ$, we consider appropriate triangulations and give a sufficient criteria for a $λ$-stable polarized toric variety $(X,L)$ to be asymptotically Chow polystable when the obstruction of asymptotic Chow semistability (the Futaki-Ono invariant) vanishes. As an application, we prove that any K-semistable polarized smooth toric variety $(X,L)$ with the vanishing Futaki-Ono invariant is asymptotically Chow polystable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06883 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chow stability of $λ$-stable toric varieties Lee, King leung Yotsutani, Naoto Algebraic Geometry Differential Geometry 51M20, 53C55, 14M25 For a given polarized toric variety, we define the notion of $λ$-stability which is a natural generalization of uniform K-stability. At the neighbourhoods of the vertices of the corresponding moment polytope $Δ$, we consider appropriate triangulations and give a sufficient criteria for a $λ$-stable polarized toric variety $(X,L)$ to be asymptotically Chow polystable when the obstruction of asymptotic Chow semistability (the Futaki-Ono invariant) vanishes. As an application, we prove that any K-semistable polarized smooth toric variety $(X,L)$ with the vanishing Futaki-Ono invariant is asymptotically Chow polystable. |
| title | Chow stability of $λ$-stable toric varieties |
| topic | Algebraic Geometry Differential Geometry 51M20, 53C55, 14M25 |
| url | https://arxiv.org/abs/2405.06883 |