Projectively flat klt varieties
[Variétés klt projectivement plates]
Journal de l’École polytechnique — Mathématiques, Tome 8 (2021) , pp. 1005-1036.

Dans le cadre des problèmes d’uniformisation, nous étudions les variétés projectives avec singularités klt dont le faisceau cotangent admet une structure projective plate sur le lieu lisse. En généralisant le travail de Jahnke-Radloff, nous montrons que les quotients des tores sont les seules variétés klt avec un faisceau cotangent semi-stable et des classes de Chern extrémales. Un résultat analogue pour les variétés avec un faisceau cotangent normalisé nef s’ensuit.

In the context of uniformisation problems, we study projective varieties with klt singularities whose cotangent sheaf admits a projectively flat structure over the smooth locus. Generalising work of Jahnke-Radloff, we show that torus quotients are the only klt varieties with semistable cotangent sheaf and extremal Chern classes. An analogous result for varieties with nef normalised cotangent sheaves follows.

Reçu le :
Accepté le :
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DOI : https://doi.org/10.5802/jep.164
Classification : 32Q30,  32Q26,  14E20,  14E30,  53B10
Mots clés : Inégalité de Bogomolov-Gieseker, variété abélienne, singularités klt, inégalité de Miyaoka-Yau, stabilité, platitude projective, uniformisation
@article{JEP_2021__8__1005_0,
     author = {Daniel Greb and Stefan Kebekus and Thomas Peternell},
     title = {Projectively flat klt varieties},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {1005--1036},
     publisher = {\'Ecole polytechnique},
     volume = {8},
     year = {2021},
     doi = {10.5802/jep.164},
     language = {en},
     url = {https://jep.centre-mersenne.org/articles/10.5802/jep.164/}
}
Daniel Greb; Stefan Kebekus; Thomas Peternell. Projectively flat klt varieties. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021) , pp. 1005-1036. doi : 10.5802/jep.164. https://jep.centre-mersenne.org/articles/10.5802/jep.164/

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