Geodesic
Symmetries and Kähler-Einstein metrics
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 605-613

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We consider Fano manifolds $M$ that admit a collection of finite automorphism groups $G_1, \ldots, G_k$ , such that the quotients $M/G_i$ are smooth Fano manifolds possessing a Kähler-Einstein metric. Under some numerical and smoothness assumptions on the ramification divisors, we prove that $M$ admits a Kähler-Einstein metric too. 
@article{BUMI_2005_8_8B_3_a4,
     author = {Arezzo, Claudio and Ghigi, Alessandro},
     title = {Symmetries and {K\"ahler-Einstein} metrics},
     journal = {Bollettino della Unione matematica italiana},
     pages = {605--613},
     publisher = {mathdoc},
     volume = {Ser. 8, 8B},
     number = {3},
     year = {2005},
     zbl = {1178.53040},
     mrnumber = {MR2182418},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a4/}
}
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Arezzo, Claudio; Ghigi, Alessandro. Symmetries and Kähler-Einstein metrics. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 605-613. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a4/