Symmetries and Kähler-Einstein metrics

Claudio Arezzo; Alessandro Ghigi

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 3, page 605-613
  • ISSN: 0392-4041

Abstract

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We consider Fano manifolds M that admit a collection of finite automorphism groups G 1 , ... , 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.

How to cite

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Arezzo, Claudio, and Ghigi, Alessandro. "Symmetries and Kähler-Einstein metrics." Bollettino dell'Unione Matematica Italiana 8-B.3 (2005): 605-613. <http://eudml.org/doc/194882>.

@article{Arezzo2005,
abstract = {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.},
author = {Arezzo, Claudio, Ghigi, Alessandro},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {605-613},
publisher = {Unione Matematica Italiana},
title = {Symmetries and Kähler-Einstein metrics},
url = {http://eudml.org/doc/194882},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Arezzo, Claudio
AU - Ghigi, Alessandro
TI - Symmetries and Kähler-Einstein metrics
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/10//
PB - Unione Matematica Italiana
VL - 8-B
IS - 3
SP - 605
EP - 613
AB - 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.
LA - eng
UR - http://eudml.org/doc/194882
ER -

References

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  9. PAUL, S. T. - TIAN, G., Analysis of geometric stability, preprint. Zbl1076.32018MR2078110
  10. RICHBERG, ROLF, Stetige streng pseudokonvexe Funktionen, Math. Ann., 175 (1968), 257-286. Zbl0153.15401MR222334
  11. TIAN, G., On Calabi’s conjecture for complex surfaces with positive first Chern class, Invent. Math., 101 (1) (1990), 101-172. Zbl0716.32019MR1055713
  12. TIAN, GANG, Kähler-Einstein metrics with positive scalar curvature, Invent. Math., 130(1) (1997), 1-37. Zbl0892.53027MR1471884
  13. GANG TIAN, , Canonical metrics in Kähler geometry, Birkhäuser Verlag, Basel, 2000. Notes taken by Meike Akveld. Zbl0978.53002MR1787650
  14. XUJIA WANG, - XIAOHUA ZHU, , Kähler-Ricci solitons on toric manifolds with positive first Chern class, 2002, preprint. Zbl1086.53067MR2084775

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