The Canonical Metric on Holomorphic Pairs over Compact Non-Kähler Manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916650736943104 |
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| author | Saito, Ryoma |
| author_facet | Saito, Ryoma |
| contents | In this paper, we prove the solvability of the vortex equation on a holomorphic vector bundle over a compact Hermitian manifold using the continuity method, and show the Kobayashi-Hitchin correspondence for holomorphic pairs. This work extends Bradlow's Kobayashi-Hitchin correspondence over compact Kähler manifolds to compact non-Kähler manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09074 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Canonical Metric on Holomorphic Pairs over Compact Non-Kähler Manifolds Saito, Ryoma Differential Geometry 53C07 (Primary) 53C55 (Secondary) In this paper, we prove the solvability of the vortex equation on a holomorphic vector bundle over a compact Hermitian manifold using the continuity method, and show the Kobayashi-Hitchin correspondence for holomorphic pairs. This work extends Bradlow's Kobayashi-Hitchin correspondence over compact Kähler manifolds to compact non-Kähler manifolds. |
| title | The Canonical Metric on Holomorphic Pairs over Compact Non-Kähler Manifolds |
| topic | Differential Geometry 53C07 (Primary) 53C55 (Secondary) |
| url | https://arxiv.org/abs/2503.09074 |