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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