Kähler-Einstein metrics on symmetric Fano T-varieties (bibtex)
by Hendrik Süß
Abstract:
Abstract We relate the global log canonical threshold of a variety with torus action to the global log canonical threshold of its quotient. We apply this to certain Fano varieties and use Tian's criterion to prove the existence of Kähler-Einstein metrics on them. In particular, we obtain simple examples of Fano threefolds being Kähler-Einstein but admitting deformations without Kähler-Einstein metric.
Reference:
Kähler-Einstein metrics on symmetric Fano T-varieties (Hendrik Süß), Advances in Mathematics, volume 246, 2013.  
Bibtex Entry:
@article{kesym,
title = "K\"ahler-Einstein metrics on symmetric Fano T-varieties ",
journal = "Advances in Mathematics",
volume = "246",
pages = "100 - 113",
year = "2013",
doi = "10.1016/j.aim.2013.06.023",
url = "http://arxiv.org/abs/1208.3597",
gsid={13564410080736942705},
author = "Hendrik S\"u\ss",
abstract = "Abstract We relate the global log canonical threshold of a variety with torus action to the global log canonical threshold of its quotient. We apply this to certain Fano varieties and use Tian's criterion to prove the existence of K\"ahler-Einstein metrics on them. In particular, we obtain simple examples of Fano threefolds being K\"ahler-Einstein but admitting deformations without K\"ahler-Einstein metric. "
}
 
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