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Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds
Journal de Mathématiques Pures et Appliquées ( IF 2.1 ) Pub Date : 2020-12-08 , DOI: 10.1016/j.matpur.2020.12.002
Thibaut Delcroix , Jakob Hultgren

We address a general system of complex Monge-Ampère equations on Fano horosymmetric manifolds and give necessary and sufficient conditions for existence of solutions in terms of combinatorial data of the manifold. This gives new results about Mabuchi metrics, twisted Kähler-Einstein metrics and coupled Kähler-Ricci solitons and provides a unified approach to many previous results on canonical metrics on Kähler manifolds.



中文翻译:

Fano 对称流形上的耦合复 Monge-Ampère 方程

我们解决了 Fano 对称流形上的复杂 Monge-Ampère 方程的一般系统,并根据流形的组合数据给出了解存在的充分必要条件。这给出了关于 Mabuchi 度量、扭曲的 Kähler-Einstein 度量和耦合的 Kähler-Ricci 孤子的新结果,并提供了对 Kähler 流形上规范度量的许多先前结果的统一方法。

更新日期:2020-12-08
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