Limits of conical Kähler-Einstein metrics on rank one horosymmetric spaces
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911901211951104 |
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| author | Delcroix, Thibaut |
| author_facet | Delcroix, Thibaut |
| contents | We consider families of conical Kähler-Einstein metrics on rank one horosymmetric Fano manifolds, with decreasing cone angles along a codimension one orbit. At the limit angle, which is positive, we show that the metrics, restricted to the complement of that orbit, converge to (the pull-back of) the Kähler-Einstein metric on the basis of the horosymmetric homogeneous space, which is a projective homogeneous space. Then we show that, on the symmetric space fibers, the rescaled metrics converge to Stenzel's Ricci flat Kähler metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_04062 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Limits of conical Kähler-Einstein metrics on rank one horosymmetric spaces Delcroix, Thibaut Differential Geometry Complex Variables 53C55, 32Q20, 32M12, We consider families of conical Kähler-Einstein metrics on rank one horosymmetric Fano manifolds, with decreasing cone angles along a codimension one orbit. At the limit angle, which is positive, we show that the metrics, restricted to the complement of that orbit, converge to (the pull-back of) the Kähler-Einstein metric on the basis of the horosymmetric homogeneous space, which is a projective homogeneous space. Then we show that, on the symmetric space fibers, the rescaled metrics converge to Stenzel's Ricci flat Kähler metrics. |
| title | Limits of conical Kähler-Einstein metrics on rank one horosymmetric spaces |
| topic | Differential Geometry Complex Variables 53C55, 32Q20, 32M12, |
| url | https://arxiv.org/abs/2310.04062 |