CIRM - Videos & books Library

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

We establish uniform estimates for Green's functions associated to Kähler forms, as the latter evolve in large families and the complex structure varies. This generalizes works of Guo, Phong, Song, and Sturm. These estimates allow one to establish diameter bounds and non-collapsing estimates for various families of canonical Kähler metrics. This is joint work with T.D.Tô.

32W20 ; 32U05 ; 32Q15 ; 35A23

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Let f : X → Y be a holomorphic map between compact Kähler manifolds. If a general fibre of f is a projective manifold a natural question is whether the morphism itself is projective, i.e. X embeds into some projectivised bundle P(V) → Y. It is well-known that this is not the case, but we will see that in some situations that are natural in the context of MMP, the answer is yes.

32J25 ; 32Q15 ; 14E30

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.

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.

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

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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

Sélection Signaler une erreur

TUTELLES

PARTENAIRES

Destination de la recherche

Raccourcis

Documents 32Q15 8 résultats

Kähler families of Green's functions - Guedj, Vincent (Auteur de la Conférence) | CIRM H Nouveau

Projectivity criteria for Kähler morphisms - Höring, Andreas (Auteur de la Conférence) | CIRM H Nouveau

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

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