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.
Si considerano varietà di Fano $M$ che ammettono un certo numero di rivestimenti di Galois $M\rightarrow M_i$, su delle varietà di Fano lisce $M_i$ che ammettono una metrica di Kähler-Einstein. Sotto alcune ipotesi numeriche sui divisori di ramificazione si dimostra che allora anche su $M$ esiste una metrica di Kähler-Einstein. 
@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 = {2212883},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a4/}
}
TY  - JOUR
AU  - Arezzo, Claudio
AU  - Ghigi, Alessandro
TI  - Symmetries and Kähler-Einstein metrics
JO  - Bollettino della Unione matematica italiana
PY  - 2005
SP  - 605
EP  - 613
VL  - 8B
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a4/
LA  - en
ID  - BUMI_2005_8_8B_3_a4
ER  - 
%0 Journal Article
%A Arezzo, Claudio
%A Ghigi, Alessandro
%T Symmetries and Kähler-Einstein metrics
%J Bollettino della Unione matematica italiana
%D 2005
%P 605-613
%V 8B
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a4/
%G en
%F BUMI_2005_8_8B_3_a4
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/

[1] C. Arezzo - A. Ghigi - G. P. Pirola, Symmetries, Quotients and Kähler-Einstein metrics, 2003, preprint. | fulltext mini-dml | MR | Zbl

[2] C. Arezzo - A. Loi, Moment maps, scalar curvature and quantization of Kähler manifolds, Comm. Math. Phys., to appear. | MR | Zbl

[3] Jean-Pierre Demailly - János Kollár, Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds, Ann. Sci. École Norm. Sup. (4), 34(4) (2001), 525-556. | fulltext mini-dml | MR | Zbl

[4] S. K. Donaldson, Scalar curvature and projective embeddings. I, J. Differential Geom., 59(3) (2001), 479-522. | fulltext mini-dml | MR | Zbl

[5] S. K. Donaldson, Scalar curvature and stability of toric varieties, J. Differential Geom., 62(2) (2002), 289-349. | fulltext mini-dml | MR | Zbl

[6] V. A. Iskovskikh - Yu. G. Prokhorov, Fano varieties. In Algebraic geometry, V, volume 47 of Encyclopaedia Math. Sci., pages 1-247, Springer, Berlin, 1999. | MR | Zbl

[7] János Kollár, Singularities of pairs. In Algebraic geometry–Santa Cruz 1995, volume 62 of Proc. Sympos. Pure Math., pages 221-287. Amer. Math. Soc., Providence, RI, 1997. | MR | Zbl

[8] Alan Michael Nadel, Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature, Ann. of Math. (2), 132(3) (1990), 549-596. | MR | Zbl

[9] S. T. Paul - G. Tian, Analysis of geometric stability, preprint. | fulltext mini-dml | MR | Zbl

[10] Rolf Richberg, Stetige streng pseudokonvexe Funktionen, Math. Ann., 175 (1968), 257-286. | MR | Zbl

[11] G. Tian, On Calabi’s conjecture for complex surfaces with positive first Chern class, Invent. Math., 101 (1) (1990), 101-172. | MR | Zbl

[12] Gang Tian, Kähler-Einstein metrics with positive scalar curvature, Invent. Math., 130(1) (1997), 1-37. | MR | Zbl

[13] Gang Tian, Canonical metrics in Kähler geometry, Birkhäuser Verlag, Basel, 2000. Notes taken by Meike Akveld. | MR | Zbl

[14] Xujia Wang - Xiaohua Zhu, Kähler-Ricci solitons on toric manifolds with positive first Chern class, 2002, preprint. | fulltext mini-dml | MR | Zbl