On the K-stability of blow-ups of projective bundles
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915063989796864 |
|---|---|
| author | Mallory, Daniel |
| author_facet | Mallory, Daniel |
| contents | We investigate the K-stability of certain blow-ups of $\mathbb{P}^1$-bundles over a Fano variety $V$, where the $\mathbb{P}^1$-bundle is the projective compactification of a line bundle $L$ proportional to $-K_V$ and the center of the blow-up is the image along a positive section of a divisor $B$ also proportional to $L$. When $V$ and $B$ are smooth, we show that, for $B \sim_{\mathbb{Q}} 2L$, the K-semistability and K-polystability of the blow-up is equivalent to the K-semistability and K-polystability of the log Fano pair $(V,aB)$ for some coefficient $a$ explicitly computed. We also show that, for $B \sim_{\mathbb{Q}} l L$, $l \neq 2$, the blow-up is K-unstable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the K-stability of blow-ups of projective bundles Mallory, Daniel Algebraic Geometry 14J45 (Primary) 32Q26 (Secondary) We investigate the K-stability of certain blow-ups of $\mathbb{P}^1$-bundles over a Fano variety $V$, where the $\mathbb{P}^1$-bundle is the projective compactification of a line bundle $L$ proportional to $-K_V$ and the center of the blow-up is the image along a positive section of a divisor $B$ also proportional to $L$. When $V$ and $B$ are smooth, we show that, for $B \sim_{\mathbb{Q}} 2L$, the K-semistability and K-polystability of the blow-up is equivalent to the K-semistability and K-polystability of the log Fano pair $(V,aB)$ for some coefficient $a$ explicitly computed. We also show that, for $B \sim_{\mathbb{Q}} l L$, $l \neq 2$, the blow-up is K-unstable. |
| title | On the K-stability of blow-ups of projective bundles |
| topic | Algebraic Geometry 14J45 (Primary) 32Q26 (Secondary) |
| url | https://arxiv.org/abs/2412.11028 |