Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913994010263552 |
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| author | Nghiem, Tran-Trung |
| author_facet | Nghiem, Tran-Trung |
| contents | We show that on every non-$G_2$ complex symmetric space of rank two, there are complete Calabi-Yau metrics of Euclidean volume growth with prescribed horospherical singular tangent cone at infinity, providing the first examples of affine Calabi-Yau smoothings of singular and irregular tangent cone. As a corollary, we obtain infinitely many examples of Calabi-Yau manifolds degenerating to the tangent cone in a single step, supporting a recent conjecture by Sun-Zhang, which was only proved when the tangent cone at infinity has only an isolated singularity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_05122 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity Nghiem, Tran-Trung Differential Geometry Algebraic Geometry 53C25, 53C55, 32Q25, 14M27 We show that on every non-$G_2$ complex symmetric space of rank two, there are complete Calabi-Yau metrics of Euclidean volume growth with prescribed horospherical singular tangent cone at infinity, providing the first examples of affine Calabi-Yau smoothings of singular and irregular tangent cone. As a corollary, we obtain infinitely many examples of Calabi-Yau manifolds degenerating to the tangent cone in a single step, supporting a recent conjecture by Sun-Zhang, which was only proved when the tangent cone at infinity has only an isolated singularity. |
| title | Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity |
| topic | Differential Geometry Algebraic Geometry 53C25, 53C55, 32Q25, 14M27 |
| url | https://arxiv.org/abs/2401.05122 |