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arXiv · 1812.07218

Coupled complex Monge-Amp\`ere equations on Fano horosymmetric manifolds

Thibaut Delcroix·Jakob Hultgren
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Abstract

We give necessary and sufficient conditions for existence of solutions to a general system of complex Monge-Amp\`ere equations on Fano horosymmetric manifolds. In particular, we get necessary and sufficient conditions for existence of coupled K\"ahler-Ricci solitons, Mabuchi metrics and twisted K\"ahler-Einstein metrics in terms of combinatorial data of the manifold.

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Thibaut Delcroix, Jakob Hultgren. 2018-12-18. Coupled complex Monge-Amp\`ere equations on Fano horosymmetric manifolds. https://doi.org/10.1016/j.matpur.2020.12.002

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