Kähler–Ricci solitons on toric manifolds with positive first Chern class. (English) Zbl 1086.53067
The authors give a complete solution to the problem of existence of Kähler-Einstein matrices or Kähler-Ricci solitons, unique up to holomorphic automorphisms, on any toric Kähler manifold with positive first Chern class. Moreover, there exists a Kähler-Ricci soliton on a compact complex surface with positive first Chern class, and a soliton is a Kähler metric if and only if the Futaki invariant vanishes. For a toric Fano manifold there exists a Kähler-Einstein metric if and only if the Futaki invariant vanishes and this implies that the holomorphic automorphism group of the manifold is reductive.
Reviewer: Jan Kurek (Lublin)
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