Polyhedral Kähler metrics on $\mathbb{CP}^n$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911404871647232 |
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| author | de Borbon, Martin Panov, Dmitri |
| author_facet | de Borbon, Martin Panov, Dmitri |
| contents | We give necessary and sufficient conditions for the existence of polyhedral Kähler metrics on $\mathbb{CP}^n$ whose singular set is a hyperplane arrangement and whose cone angles are in $(0, 2π)$. These conditions take the form of linear and quadratic constraints on the cone angles and are entirely determined by the intersection poset of the arrangement. Our proof of existence relies on a parabolic version of the Kobayashi-Hitchin correspondence, due to T. Mochizuki. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polyhedral Kähler metrics on $\mathbb{CP}^n$ de Borbon, Martin Panov, Dmitri Differential Geometry Algebraic Geometry We give necessary and sufficient conditions for the existence of polyhedral Kähler metrics on $\mathbb{CP}^n$ whose singular set is a hyperplane arrangement and whose cone angles are in $(0, 2π)$. These conditions take the form of linear and quadratic constraints on the cone angles and are entirely determined by the intersection poset of the arrangement. Our proof of existence relies on a parabolic version of the Kobayashi-Hitchin correspondence, due to T. Mochizuki. |
| title | Polyhedral Kähler metrics on $\mathbb{CP}^n$ |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2510.17447 |