Gauduchon metrics and Hermite-Einstein metrics on non-Kähler varieties
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866913718485385216 |
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| author | Pan, Chung-Ming |
| author_facet | Pan, Chung-Ming |
| contents | We show the existence of Gauduchon metrics on arbitrary compact hermitian varieties, generalizing our previous work on smoothable singularities. These metrics allow us to define the notion of slope stability for torsion-free coherent sheaves on compact normal varieties that are not necessarily Kähler. Then we prove the existence and uniqueness of singular Hermite-Einstein metrics for slope-stable reflexive sheaves on non-Kähler normal varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gauduchon metrics and Hermite-Einstein metrics on non-Kähler varieties Pan, Chung-Ming Differential Geometry Algebraic Geometry Complex Variables We show the existence of Gauduchon metrics on arbitrary compact hermitian varieties, generalizing our previous work on smoothable singularities. These metrics allow us to define the notion of slope stability for torsion-free coherent sheaves on compact normal varieties that are not necessarily Kähler. Then we prove the existence and uniqueness of singular Hermite-Einstein metrics for slope-stable reflexive sheaves on non-Kähler normal varieties. |
| title | Gauduchon metrics and Hermite-Einstein metrics on non-Kähler varieties |
| topic | Differential Geometry Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2503.02759 |