A Note On Kähler-Ricci Flow on Fano Threefolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914467907895296 |
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| author | Miao, Minghao Tian, Gang |
| author_facet | Miao, Minghao Tian, Gang |
| contents | In this note, we show that the solution of Kähler-Ricci flow on every Fano threefold from the family No.2.23 in the Mori-Mukai's list develops type II singularity. In fact, we show that no Fano threefold from the family No.2.23 admits Kähler-Ricci soliton and the Gromov-Hausdorff limit of the Kähler-Ricci flow must be a singular $\mathbb{Q}$-Fano variety. This gives new examples of Fano manifolds of the lowest dimension on which Kähler-Ricci flow develops type II singularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_15263 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Note On Kähler-Ricci Flow on Fano Threefolds Miao, Minghao Tian, Gang Differential Geometry Algebraic Geometry Complex Variables 53E30, 32Q26, 53C25, 32Q20 In this note, we show that the solution of Kähler-Ricci flow on every Fano threefold from the family No.2.23 in the Mori-Mukai's list develops type II singularity. In fact, we show that no Fano threefold from the family No.2.23 admits Kähler-Ricci soliton and the Gromov-Hausdorff limit of the Kähler-Ricci flow must be a singular $\mathbb{Q}$-Fano variety. This gives new examples of Fano manifolds of the lowest dimension on which Kähler-Ricci flow develops type II singularity. |
| title | A Note On Kähler-Ricci Flow on Fano Threefolds |
| topic | Differential Geometry Algebraic Geometry Complex Variables 53E30, 32Q26, 53C25, 32Q20 |
| url | https://arxiv.org/abs/2210.15263 |