Kaehler-Ricci Solitons on Toric Fano Varieties

摘要

In this paper, the authors discuss the existence of Kahler-Ricci soliton byreducing to solve certain complex Monge-Ampere equation on a compact complex manifold with positive first Chern class, especially on a toric Fanno variety. As similar as the study of Kahler-Einstein metrics, one can use continuity method to solve such a complex Monge-Ampere equation. In fact, many places can be modified as in the proof of uniqueness ((bar)TZ2) although some new difficulties will arise. The purpose of this paper is to give an approach to solve these difficulties.