Kahler-Einstein metrics on symmetric Fano T-varieties

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 Kahler-Einstein metrics on them. In particular, we obtain simple examples of Fano threefolds being Kahler-Einstein but admitting deformations without Kahler-Einstein metric.

12 pages, main theorem slightly improved + minor corrections

References in corpus (4)

• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• On Chow quotients of torus actions
• Deformations of extremal toric manifolds
• Quotients of an affine variety by an action of a torus

Cited by in corpus (8)

• K-Stability for Fano Manifolds with Torus Action of Complexity One
• Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds
• Fano threefolds with infinite automorphism groups
• Kähler-Einstein metrics along the smooth continuity method
• Delta-invariants for Fano varieties with large automorphism groups
• Geometric quantization of coupled Kähler-Einstein metrics
• Remarks on Mukai threefolds admitting $C^{\ast }$ action
• Fano threefolds with 2-torus action - a picture book