Miyaoka-Yau inequalities and the topological characterization of certain klt varieties
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913429148663808 |
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| author | Greb, Daniel Kebekus, Stefan Peternell, Thomas |
| author_facet | Greb, Daniel Kebekus, Stefan Peternell, Thomas |
| contents | Ball quotients, hyperelliptic varieties, and projective spaces are characterized by their Chern classes, as the varieties where the Miyaoka-Yau inequality becomes an equality. Ball quotients, Abelian varieties, and projective spaces are also characterized topologically: if a complex, projective manifold $X$ is homeomorphic to a variety of this type, then $X$ is itself of this type. In this paper, similar results are established for projective varieties with klt singularities that are homeomorphic to singular ball quotients, quotients of Abelian varieties, or projective spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14121 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Miyaoka-Yau inequalities and the topological characterization of certain klt varieties Greb, Daniel Kebekus, Stefan Peternell, Thomas Algebraic Geometry Complex Variables 32Q30, 32Q26, 14E20, 14E30 Ball quotients, hyperelliptic varieties, and projective spaces are characterized by their Chern classes, as the varieties where the Miyaoka-Yau inequality becomes an equality. Ball quotients, Abelian varieties, and projective spaces are also characterized topologically: if a complex, projective manifold $X$ is homeomorphic to a variety of this type, then $X$ is itself of this type. In this paper, similar results are established for projective varieties with klt singularities that are homeomorphic to singular ball quotients, quotients of Abelian varieties, or projective spaces. |
| title | Miyaoka-Yau inequalities and the topological characterization of certain klt varieties |
| topic | Algebraic Geometry Complex Variables 32Q30, 32Q26, 14E20, 14E30 |
| url | https://arxiv.org/abs/2309.14121 |