Extremal Kähler metrics on blowups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916414985601024 |
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| author | Dervan, Ruadhaí Sektnan, Lars Martin |
| author_facet | Dervan, Ruadhaí Sektnan, Lars Martin |
| contents | Consider a compact Kähler manifold which either admits an extremal Kähler metric, or is a small deformation of such a manifold. We show that the blowup of the manifold at a point admits an extremal Kähler metric in Kähler classes making the exceptional divisor sufficiently small if and only if it is relatively K-stable, as predicted by the Yau-Tian-Donaldson conjecture. We also give a geometric interpretation of what relative K-stability means in this case in terms of finite dimensional geometric invariant theory. This gives a complete solution to a problem introduced and solved by Arezzo, Pacard, Singer and Székelyhidi for constant scalar curvature Kähler metrics in dimension at least three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_13579 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Extremal Kähler metrics on blowups Dervan, Ruadhaí Sektnan, Lars Martin Differential Geometry Algebraic Geometry Consider a compact Kähler manifold which either admits an extremal Kähler metric, or is a small deformation of such a manifold. We show that the blowup of the manifold at a point admits an extremal Kähler metric in Kähler classes making the exceptional divisor sufficiently small if and only if it is relatively K-stable, as predicted by the Yau-Tian-Donaldson conjecture. We also give a geometric interpretation of what relative K-stability means in this case in terms of finite dimensional geometric invariant theory. This gives a complete solution to a problem introduced and solved by Arezzo, Pacard, Singer and Székelyhidi for constant scalar curvature Kähler metrics in dimension at least three. |
| title | Extremal Kähler metrics on blowups |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2110.13579 |