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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2601.15138 |
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| _version_ | 1866911417487065088 |
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| author | Müller, Niklas |
| author_facet | Müller, Niklas |
| contents | In this paper we present, for any integers $0\leq ν\leq n$, a set of inequalities satisfied by the Chern classes of any minimal complex projective variety of dimension $n$ and numerical dimension $ν$. In the cases where $ν$ is either very small or very large compared with $n$, this recovers many previously known results. We demonstrate that our inequalities are sharp by providing an explicit characterisation of those varieties achieving the equality; our proof, in particular, resolves the Abundance conjecture in this situation. Additionally, we provide some new examples of varieties with extremal Chern classes that demonstrate the optimality of our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15138 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inequalities of Miyaoka-Yau type $\&$ Uniformisation of varieties of intermediate Kodaira Dimension Müller, Niklas Algebraic Geometry In this paper we present, for any integers $0\leq ν\leq n$, a set of inequalities satisfied by the Chern classes of any minimal complex projective variety of dimension $n$ and numerical dimension $ν$. In the cases where $ν$ is either very small or very large compared with $n$, this recovers many previously known results. We demonstrate that our inequalities are sharp by providing an explicit characterisation of those varieties achieving the equality; our proof, in particular, resolves the Abundance conjecture in this situation. Additionally, we provide some new examples of varieties with extremal Chern classes that demonstrate the optimality of our results. |
| title | Inequalities of Miyaoka-Yau type $\&$ Uniformisation of varieties of intermediate Kodaira Dimension |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.15138 |