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.
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@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/}
}
TY - JOUR AU - Daniel Greb AU - Stefan Kebekus AU - Thomas Peternell TI - Projectively flat klt varieties JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 1005 EP - 1036 VL - 8 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.164/ DO - 10.5802/jep.164 LA - en ID - JEP_2021__8__1005_0 ER -
%0 Journal Article %A Daniel Greb %A Stefan Kebekus %A Thomas Peternell %T Projectively flat klt varieties %J Journal de l’École polytechnique — Mathématiques %D 2021 %P 1005-1036 %V 8 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.164/ %R 10.5802/jep.164 %G en %F JEP_2021__8__1005_0
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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