The Kobayashi-Hitchin correspondence for nef and big classes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917550008303616 |
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| author | Jinnouchi, Satoshi |
| author_facet | Jinnouchi, Satoshi |
| contents | In this paper, we establish the Kobayashi-Hitchin correspondence for nef and big cohomology classes by introducing the notions of adapted closed positive $(1,1)$-currents and adapted Hermitian-Yang-Mills metrics. As applications, we investigate the equality cases of both the Bogomolov-Gieseker inequality for semistable reflexive sheaves with respect to big classes admitting a bimeromorphic Zariski decomposition and the Miyaoka-Yau inequality for projective varieties with big anti-canonical divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10312 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Kobayashi-Hitchin correspondence for nef and big classes Jinnouchi, Satoshi Differential Geometry Algebraic Geometry Complex Variables 53C07, 32J25, 32W20 In this paper, we establish the Kobayashi-Hitchin correspondence for nef and big cohomology classes by introducing the notions of adapted closed positive $(1,1)$-currents and adapted Hermitian-Yang-Mills metrics. As applications, we investigate the equality cases of both the Bogomolov-Gieseker inequality for semistable reflexive sheaves with respect to big classes admitting a bimeromorphic Zariski decomposition and the Miyaoka-Yau inequality for projective varieties with big anti-canonical divisor. |
| title | The Kobayashi-Hitchin correspondence for nef and big classes |
| topic | Differential Geometry Algebraic Geometry Complex Variables 53C07, 32J25, 32W20 |
| url | https://arxiv.org/abs/2603.10312 |