Weighted extremal metrics on blowups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916722977538048 |
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| author | Hallam, Michael |
| author_facet | Hallam, Michael |
| contents | We show that if a compact Kähler manifold admits a weighted extremal metric for the action of a torus, so too does its blowup at a relatively stable point that is fixed by both the torus action and the extremal field. This generalises previous results on extremal metrics by Arezzo--Pacard--Singer and Székelyhidi to many other canonical metrics, including extremal Sasaki metrics, deformations of Kähler--Ricci solitons and $μ$-cscK metrics. In a sequel to this paper, we use this result to study the weighted K-stability of weighted extremal manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08338 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weighted extremal metrics on blowups Hallam, Michael Differential Geometry 53C55 We show that if a compact Kähler manifold admits a weighted extremal metric for the action of a torus, so too does its blowup at a relatively stable point that is fixed by both the torus action and the extremal field. This generalises previous results on extremal metrics by Arezzo--Pacard--Singer and Székelyhidi to many other canonical metrics, including extremal Sasaki metrics, deformations of Kähler--Ricci solitons and $μ$-cscK metrics. In a sequel to this paper, we use this result to study the weighted K-stability of weighted extremal manifolds. |
| title | Weighted extremal metrics on blowups |
| topic | Differential Geometry 53C55 |
| url | https://arxiv.org/abs/2304.08338 |