Equality in the Miyaoka–Yau inequality and uniformization of non-positively curved klt pairs
Let $(X, \Delta )$ be a compact Kähler klt pair, where $K_X + \Delta $ is ample or numerically trivial, and $\Delta $ has standard coefficients. We show that if equality holds in the orbifold Miyaoka–Yau inequality for $(X, \Delta )$, then its orbifold universal cover is either the unit ball (ample...
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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.599/ |
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| author | Claudon, Benoît Graf, Patrick Guenancia, Henri |
| author_facet | Claudon, Benoît Graf, Patrick Guenancia, Henri |
| author_sort | Claudon, Benoît |
| collection | DOAJ |
| description | Let $(X, \Delta )$ be a compact Kähler klt pair, where $K_X + \Delta $ is ample or numerically trivial, and $\Delta $ has standard coefficients. We show that if equality holds in the orbifold Miyaoka–Yau inequality for $(X, \Delta )$, then its orbifold universal cover is either the unit ball (ample case) or the affine space (numerically trivial case). |
| format | Article |
| id | doaj-art-8d13e760c0d24a40beaf4c8784f97ce5 |
| 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-8d13e760c0d24a40beaf4c8784f97ce52025-02-07T11:13:30ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-06-01362S1558110.5802/crmath.59910.5802/crmath.599Equality in the Miyaoka–Yau inequality and uniformization of non-positively curved klt pairsClaudon, Benoît0Graf, Patrick1Guenancia, Henri2Univ Rennes, CNRS, IRMAR – UMR 6625, 35000 Rennes, France et Institut Universitaire de FranceLehrstuhl für Mathematik I, Universität Bayreuth, 95440 Bayreuth, GermanyInstitut de Mathématiques de Toulouse, Université Paul Sabatier, 31062 Toulouse Cedex 9, FranceLet $(X, \Delta )$ be a compact Kähler klt pair, where $K_X + \Delta $ is ample or numerically trivial, and $\Delta $ has standard coefficients. We show that if equality holds in the orbifold Miyaoka–Yau inequality for $(X, \Delta )$, then its orbifold universal cover is either the unit ball (ample case) or the affine space (numerically trivial case).https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.599/Miyaoka–Yau inequalityorbifold uniformizationklt pairs |
| spellingShingle | Claudon, Benoît Graf, Patrick Guenancia, Henri Equality in the Miyaoka–Yau inequality and uniformization of non-positively curved klt pairs Comptes Rendus. Mathématique Miyaoka–Yau inequality orbifold uniformization klt pairs |
| title | Equality in the Miyaoka–Yau inequality and uniformization of non-positively curved klt pairs |
| title_full | Equality in the Miyaoka–Yau inequality and uniformization of non-positively curved klt pairs |
| title_fullStr | Equality in the Miyaoka–Yau inequality and uniformization of non-positively curved klt pairs |
| title_full_unstemmed | Equality in the Miyaoka–Yau inequality and uniformization of non-positively curved klt pairs |
| title_short | Equality in the Miyaoka–Yau inequality and uniformization of non-positively curved klt pairs |
| title_sort | equality in the miyaoka yau inequality and uniformization of non positively curved klt pairs |
| topic | Miyaoka–Yau inequality orbifold uniformization klt pairs |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.599/ |
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