Let be an abelian variety, and a finite group acting freely in codimension two. We discuss whether the singular quotient admits a resolution that is a Calabi-Yau manifold. While Oguiso constructed two examples in dimension 3, we show that there are none in dimension 4. We also classify up to isogeny the possible abelian varieties in arbitrary dimension.
Soit une variété abélienne et un groupe fini agissant librement en codimension par automorphismes sur . On s’intéresse ici aux conditions d’existence d’une résolution du quotient singulier qui soit une variété de Calabi-Yau. Tandis qu’en dimension , deux exemples de quotients admettant une telle résolution ont été construits par Oguiso dans un article de 1994, on montre ici qu’aucun quotient de la sorte n’existe en dimension . En dimension quelconque, on classifie les variétés abéliennes susceptibles d’admettre des quotients de la sorte, à isogénie près.
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Keywords: Crepant resolution, abelian variety with complex multiplication, Calabi-Yau manifold
Mot clés : Résolution crépante, variété abélienne à multiplication complexe, variété de Calabi-Yau
Cécile Gachet 1
@article{JEP_2024__11__1219_0, author = {C\'ecile Gachet}, title = {Finite quotients of abelian varieties with {a~Calabi-Yau} resolution}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {1219--1286}, publisher = {\'Ecole polytechnique}, volume = {11}, year = {2024}, doi = {10.5802/jep.277}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.277/} }
TY - JOUR AU - Cécile Gachet TI - Finite quotients of abelian varieties with a Calabi-Yau resolution JO - Journal de l’École polytechnique — Mathématiques PY - 2024 SP - 1219 EP - 1286 VL - 11 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.277/ DO - 10.5802/jep.277 LA - en ID - JEP_2024__11__1219_0 ER -
%0 Journal Article %A Cécile Gachet %T Finite quotients of abelian varieties with a Calabi-Yau resolution %J Journal de l’École polytechnique — Mathématiques %D 2024 %P 1219-1286 %V 11 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.277/ %R 10.5802/jep.277 %G en %F JEP_2024__11__1219_0
Cécile Gachet. Finite quotients of abelian varieties with a Calabi-Yau resolution. Journal de l’École polytechnique — Mathématiques, Volume 11 (2024), pp. 1219-1286. doi : 10.5802/jep.277. https://jep.centre-mersenne.org/articles/10.5802/jep.277/
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