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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2402.04021 |
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| _version_ | 1866911772113371136 |
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| author | Hitchin, Nigel |
| author_facet | Hitchin, Nigel |
| contents | We consider the twistor theory approach to Kronheimer's ALE metrics on resolutions of the quotient of C^2 by a finite subgroup of SU(2). The circle action on the 4-manifold induces a C^* action on a compactification of the twistor space and we identify the orbit of a generic twistor line as a nodal rational curve in a particular cohomology class of a projective rational surface. Using the results of N.Honda et al we identify this surface with the minitwistor space for the Einstein-Weyl structure on the 3-dimensional quotient of the ALE space by the circle action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04021 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | ALE spaces and nodal curves Hitchin, Nigel Differential Geometry 53C26, 53C18, 14J42 We consider the twistor theory approach to Kronheimer's ALE metrics on resolutions of the quotient of C^2 by a finite subgroup of SU(2). The circle action on the 4-manifold induces a C^* action on a compactification of the twistor space and we identify the orbit of a generic twistor line as a nodal rational curve in a particular cohomology class of a projective rational surface. Using the results of N.Honda et al we identify this surface with the minitwistor space for the Einstein-Weyl structure on the 3-dimensional quotient of the ALE space by the circle action. |
| title | ALE spaces and nodal curves |
| topic | Differential Geometry 53C26, 53C18, 14J42 |
| url | https://arxiv.org/abs/2402.04021 |