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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2304.08338 |
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- 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.