Uniform K-stability of polarized spherical varieties
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912980498644992 |
|---|---|
| author | Delcroix, Thibaut |
| author_facet | Delcroix, Thibaut |
| contents | We express notions of K-stability of polarized spherical varieties in terms of combinatorial data, vastly generalizing the case of toric varieties. We then provide a combinatorial sufficient condition of G-uniform K-stability by studying the corresponding convex geometric problem. Thanks to recent work of Chi Li and a remark by Yuji Odaka, this provides an explicitly checkable sufficient condition of existence of constant scalar curvature Kahler metrics. As a side effect, we show that, on several families of spherical varieties, G-uniform K-stability is equivalent to K-polystability with respect to G-equivariant test configurations for polarizations close to the anticanonical bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_06463 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Uniform K-stability of polarized spherical varieties Delcroix, Thibaut Algebraic Geometry Complex Variables Differential Geometry 14M27, 32Q26, 53C25, 32Q20 We express notions of K-stability of polarized spherical varieties in terms of combinatorial data, vastly generalizing the case of toric varieties. We then provide a combinatorial sufficient condition of G-uniform K-stability by studying the corresponding convex geometric problem. Thanks to recent work of Chi Li and a remark by Yuji Odaka, this provides an explicitly checkable sufficient condition of existence of constant scalar curvature Kahler metrics. As a side effect, we show that, on several families of spherical varieties, G-uniform K-stability is equivalent to K-polystability with respect to G-equivariant test configurations for polarizations close to the anticanonical bundle. |
| title | Uniform K-stability of polarized spherical varieties |
| topic | Algebraic Geometry Complex Variables Differential Geometry 14M27, 32Q26, 53C25, 32Q20 |
| url | https://arxiv.org/abs/2009.06463 |