We propose new types of canonical metrics on K\ue4hler manifolds, called coupled K\ue4hler–Einstein metrics, generalizing K\ue4hler–Einstein metrics. We prove existence and uniqueness results in the cases when the canonical bundle is ample and when the manifold is K\ue4hler–Einstein Fano. In the Fano case, we also prove that existence of coupled K\ue4hler–Einstein metrics imply a certain algebraic stability condition, generalizing K-polystability
We study the existence of extremal Kähler metrics on Kähler manifolds. After introducing a notion of...
In this article we prove the existence of Kähler–Einstein metrics on Q-Gorenstein smoothable, K-poly...
We announce a proof of the fact that a K-stable Fano manifold admits a Kähler–Einstein metric and g...
We present classical and recent results on Kähler-Einstein metrics on compact complex manifolds, foc...
We consider Fano manifolds M that admit a collection of finite automorphism groups G1, ...,Gk, such ...
It is shown that any, possibly singular, Fano variety X admitting a Kahler-Einstein metric is K-poly...
We prove that if a Fano manifold M is K-stable, then it admits a Kahler-Einstein metric. It affirms ...
Let X be a canonically polarized variety, i.e. a complex projective variety such that its canonical ...
This volume is an outcome of the workshop "Moduli of K-stable Varieties", which was held in Rome, It...
This is an expository paper on Kahler metrics of positive scalar curvature. It is for my Takagi Lect...
Let X be a canonically polarized variety, i.e. a complex projective variety such that its canonical ...
We give an elementary treatment of the existence of complete Kähler–Einstein metrics with nonpositiv...
We prove a necessary and sufficient condition in terms of the barycenters of a collection of polytop...
We give an elementary treatment of the existence of complete Kähler–Einstein metrics with nonpositiv...
International audienceLet Y be a compact Kähler normal space and α ∈ H1,1BC (Y) a Kähler class. We s...
We study the existence of extremal Kähler metrics on Kähler manifolds. After introducing a notion of...
In this article we prove the existence of Kähler–Einstein metrics on Q-Gorenstein smoothable, K-poly...
We announce a proof of the fact that a K-stable Fano manifold admits a Kähler–Einstein metric and g...
We present classical and recent results on Kähler-Einstein metrics on compact complex manifolds, foc...
We consider Fano manifolds M that admit a collection of finite automorphism groups G1, ...,Gk, such ...
It is shown that any, possibly singular, Fano variety X admitting a Kahler-Einstein metric is K-poly...
We prove that if a Fano manifold M is K-stable, then it admits a Kahler-Einstein metric. It affirms ...
Let X be a canonically polarized variety, i.e. a complex projective variety such that its canonical ...
This volume is an outcome of the workshop "Moduli of K-stable Varieties", which was held in Rome, It...
This is an expository paper on Kahler metrics of positive scalar curvature. It is for my Takagi Lect...
Let X be a canonically polarized variety, i.e. a complex projective variety such that its canonical ...
We give an elementary treatment of the existence of complete Kähler–Einstein metrics with nonpositiv...
We prove a necessary and sufficient condition in terms of the barycenters of a collection of polytop...
We give an elementary treatment of the existence of complete Kähler–Einstein metrics with nonpositiv...
International audienceLet Y be a compact Kähler normal space and α ∈ H1,1BC (Y) a Kähler class. We s...
We study the existence of extremal Kähler metrics on Kähler manifolds. After introducing a notion of...
In this article we prove the existence of Kähler–Einstein metrics on Q-Gorenstein smoothable, K-poly...
We announce a proof of the fact that a K-stable Fano manifold admits a Kähler–Einstein metric and g...
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