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Coupled Kähler-Einstein Metrics

Journal article
Authors Jakob Hultgren
David Witt Nyström
Published in International mathematics research notices
ISSN 1073-7928
Publication year 2018
Published at Department of Mathematical Sciences
Language en
Subject categories Geometry


We propose new types of canonical metrics on Kähler manifolds, called coupled Kähler–Einstein metrics, generalizing Kähler–Einstein metrics. We prove existence and uniqueness results in the cases when the canonical bundle is ample and when the manifold is Kähler–Einstein Fano. In the Fano case, we also prove that existence of coupled Kähler–Einstein metrics imply a certain algebraic stability condition, generalizing K-polystability.

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