CIRM - Videos & books Library

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

We develop a parabolic pluripotential theory on compact Kähler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Ampere equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the Kähler-Ricci flow on varieties with log terminal singularities.

53C44 ; 32W20 ; 58J35

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Let $f : X \to Y$ be a fibration between two projective manifolds. The Iitaka's conjecture predicts that the Kodaira dimension of $X$ is larger than the sum of the Kodaira dimension of $X$ and the Kodaira dimension of the generic fiber. We explain a proof of the Iitaka conjecture for algebraic fiber spaces over abelian varieties or projective surfaces.
It is a joint work with Mihai Paun.

14E30 ; 14K05 ; 14J10

Sélection Signaler une erreur

TUTELLES

PARTENAIRES

Destination de la recherche

Raccourcis

Documents Di Nezza, Eleonora 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

Pluripotential Kähler-Ricci flows - Guedj, Vincent (Auteur de la Conférence) | CIRM H Nouveau

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

Kodaira dimension of algebraic fiber spaces over abelian varieties or projective surfaces - Cao, Junyan (Auteur de la Conférence) | CIRM H Nouveau

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