Mabuchi Kähler solitons versus extremal Kähler metrics and beyond
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917881796624384 |
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| author | Apostolov, Vestislav Lahdili, Abdellah Nitta, Yasufumi |
| author_facet | Apostolov, Vestislav Lahdili, Abdellah Nitta, Yasufumi |
| contents | Using the Yau-Tian-Donaldson type correspondence for $v$-solitons established by Han-Li, we show that a smooth complex $n$-dimensional Fano variety admits a Mabuchi soliton provided it admits an extremal Kähler metric whose scalar curvature is strictly less than $2(n+1)$. Combined with previous observations by Mabuchi and Nakamura in the other direction, this gives a characterization of the existence of Mabuchi solitons in terms of the existence of extremal Kähler metrics on Fano manifolds. An extension of this correspondence to $v$-solitons is also obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01871 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mabuchi Kähler solitons versus extremal Kähler metrics and beyond Apostolov, Vestislav Lahdili, Abdellah Nitta, Yasufumi Differential Geometry Algebraic Geometry Using the Yau-Tian-Donaldson type correspondence for $v$-solitons established by Han-Li, we show that a smooth complex $n$-dimensional Fano variety admits a Mabuchi soliton provided it admits an extremal Kähler metric whose scalar curvature is strictly less than $2(n+1)$. Combined with previous observations by Mabuchi and Nakamura in the other direction, this gives a characterization of the existence of Mabuchi solitons in terms of the existence of extremal Kähler metrics on Fano manifolds. An extension of this correspondence to $v$-solitons is also obtained. |
| title | Mabuchi Kähler solitons versus extremal Kähler metrics and beyond |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2407.01871 |