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We proved that any K-semistable log Fano cone admits a special degeneration to a uniquely determined K-polystable log Fano cone. This confirms a conjecture of Donaldson-Sun stating that the metric tangent cone of any close point appearing on a Gromov-Hausdorff limit of Kähler-Einstein Fano manifolds depends only on the algebraic structure of the singularity. This is a joint work with Chi Li and Chenyang Xu.

14J45 ; 32Q15 ; 32Q20 ; 53C55

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One of the central problems in algebraic geometry is to form a reasonable (e.g. Hausdorff) moduli space of smooth polarised varieties. I will show how one can solve this problem using canonical Kähler metrics. This is joint work with Philipp Naumann.

14D20 ; 32Q15 ; 53C55

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We develop apriori estimates for scalar curvature type equations on compact Kähler manifolds. As an application, we show that K-energy being proper with respect to $L^1$ geodesic distance implies the existence of constant scalar curvature Kähler metrics. This is joint work with Xiuxiong Chen.

53C55 ; 32Q20 ; 32Q15

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I will present some results about the momentum polytopes of the multiplicity-free Hamiltonian compact manifolds acted on by a compact group which are Kählerizable. I shall give a characterization of these polytopes, explain how much they determine these manifolds and sketch some applications of this characterization – most of these results have been obtained jointly with G. Pezzini and B. Van Steirteghem.

14M27 ; 53D20 ; 32Q15

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Let $(V,\omega)$ be a compact Kähler manifold and $X$ be an analytic subvariety of $V$. We address the problem of extending $\omega$-plurisubharmonic functions on $X$ to $\omega$-plurisubharmonic functions on $V$. Our results are joint with Vincent Guedj and Ahmed Zeriahi.

32U05 ; 31C10 ; 32C25 ; 32Q15 ; 32Q28

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Since the proof of the Calabi conjecture given by Yau, complex Monge-Ampère equations on compact Kähler manifolds have been intensively studied.
In this talk we consider complex Monge-Ampère equations with prescribed singularities. More precisely, we fix a potential and we show existence and uniqueness of solutions of complex Monge-Ampère equations which have the same singularity type of the model potential we chose. This result can be interpreted as a generalisation of Yau's theorem (in this case the model potential is smooth).
As a corollary we obtain the existence of singular Kähler-Einstein metrics with prescribed singularities on general type and Calabi-Yau manifolds.
This is a joint work with Tamas Darvas and Chinh Lu.[-]

Since the proof of the Calabi conjecture given by Yau, complex Monge-Ampère equations on compact Kähler manifolds have been intensively studied.
In this talk we consider complex Monge-Ampère equations with prescribed singularities. More precisely, we fix a potential and we show existence and uniqueness of solutions of complex Monge-Ampère equations which have the same singularity type of the model potential we chose. This result can be ...[+]

32J27 ; 32Q15 ; 32Q20 ; 32W20

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Documents 32Q15 6 résultats

Algebraicity of the metric tangent cones - Wang, Xiaowei (Auteur de la Conférence) | CIRM H Nouveau

Moduli of algebraic varieties - Dervan, Ruadhai (Auteur de la Conférence) | CIRM H Nouveau

Apriori estimates for scalar curvature type equations on compact Kähler manifolds - Cheng, Jingrui (Auteur de la Conférence) | CIRM H Nouveau

Momentum polytopes of Kähler compact multiplicity-free manifolds - Cupit-Foutou, Stéphanie (Auteur de la Conférence) | CIRM H Nouveau

Extension of quasiplurisubharmonic functions - Coman, Dan (Auteur de la Conférence) | CIRM H Nouveau

Complex Monge-Ampere equations with prescribed singularities​ - Di Nezza, Eleonora (Auteur de la Conférence) | CIRM H Nouveau

Complex Monge-Ampere equations with prescribed singularities - Di Nezza, Eleonora (Auteur de la Conférence) | CIRM H Nouveau