Miyaoka–Yau inequalities and the topological characterization of certain klt varieties
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 mani...
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| Format: | Article |
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Académie des sciences
2024-06-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.580/ |
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| author | Greb, Daniel Kebekus, Stefan Peternell, Thomas |
| author_facet | Greb, Daniel Kebekus, Stefan Peternell, Thomas |
| author_sort | Greb, Daniel |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-7af4f8d639334518a1125cbf156de6b4 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-7af4f8d639334518a1125cbf156de6b42025-02-07T11:13:30ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-06-01362S114115710.5802/crmath.58010.5802/crmath.580Miyaoka–Yau inequalities and the topological characterization of certain klt varietiesGreb, Daniel0Kebekus, Stefan1Peternell, Thomas2Essener Seminar für Algebraische Geometrie und Arithmetik, Fakultät für Mathematik, Universität Duisburg–Essen, 45117 Essen, GermanyMathematisches Institut, Albert-Ludwigs-Universität Freiburg, Ernst-Zermelo-Straße 1, 79104 Freiburg im Breisgau, GermanyMathematisches Institut, Universität Bayreuth, 95440 Bayreuth, GermanyBall 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.580/Miyaoka–Yau inequalityklt singularitiesuniformisationhomeomorphisms |
| spellingShingle | Greb, Daniel Kebekus, Stefan Peternell, Thomas Miyaoka–Yau inequalities and the topological characterization of certain klt varieties Comptes Rendus. Mathématique Miyaoka–Yau inequality klt singularities uniformisation homeomorphisms |
| title | Miyaoka–Yau inequalities and the topological characterization of certain klt varieties |
| title_full | Miyaoka–Yau inequalities and the topological characterization of certain klt varieties |
| title_fullStr | Miyaoka–Yau inequalities and the topological characterization of certain klt varieties |
| title_full_unstemmed | Miyaoka–Yau inequalities and the topological characterization of certain klt varieties |
| title_short | Miyaoka–Yau inequalities and the topological characterization of certain klt varieties |
| title_sort | miyaoka yau inequalities and the topological characterization of certain klt varieties |
| topic | Miyaoka–Yau inequality klt singularities uniformisation homeomorphisms |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.580/ |
| work_keys_str_mv | AT grebdaniel miyaokayauinequalitiesandthetopologicalcharacterizationofcertainkltvarieties AT kebekusstefan miyaokayauinequalitiesandthetopologicalcharacterizationofcertainkltvarieties AT peternellthomas miyaokayauinequalitiesandthetopologicalcharacterizationofcertainkltvarieties |