Weighted extremal Kähler metrics on resolutions of singularities
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908639397150720 |
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| author | Boucksom, Sébastien Jonsson, Mattias Trusiani, Antonio |
| author_facet | Boucksom, Sébastien Jonsson, Mattias Trusiani, Antonio |
| contents | Generalizing previous results of Arezzo-Pacard-Singer, Seyyedali-Székelyhidi and Hallam, we prove the invariance under smooth blowups of the class of weighted extremal Kähler manifolds, modulo a log-concavity assumption on the first weight. Through recent work of Di Nezza-Jubert-Lahdili and Han-Liu, this is obtained as a consequence of a general uniform coercivity estimate for the (relative, weighted) Mabuchi energy on the blowup, which applies more generally to any equivariant resolution of singularities of Fano type of a compact Kähler klt space whose Mabuchi energy is assumed to be coercive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted extremal Kähler metrics on resolutions of singularities Boucksom, Sébastien Jonsson, Mattias Trusiani, Antonio Differential Geometry 58E11, 53C55, 32U05 Generalizing previous results of Arezzo-Pacard-Singer, Seyyedali-Székelyhidi and Hallam, we prove the invariance under smooth blowups of the class of weighted extremal Kähler manifolds, modulo a log-concavity assumption on the first weight. Through recent work of Di Nezza-Jubert-Lahdili and Han-Liu, this is obtained as a consequence of a general uniform coercivity estimate for the (relative, weighted) Mabuchi energy on the blowup, which applies more generally to any equivariant resolution of singularities of Fano type of a compact Kähler klt space whose Mabuchi energy is assumed to be coercive. |
| title | Weighted extremal Kähler metrics on resolutions of singularities |
| topic | Differential Geometry 58E11, 53C55, 32U05 |
| url | https://arxiv.org/abs/2412.06096 |