The Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds - Université de Montpellier Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

The Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds

Thibaut Delcroix

Résumé

We prove the Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds, that is, for projective manifolds equipped with a holomorphic action of a compact Lie group with at least one real hypersurface orbit. Contrary to what seems to be a popular belief, such manifolds do not admit extremal Kähler metrics in all Kähler classes in general. More generally, we prove that for rank one polarized spherical varieties, G-uniform K-stability is equivalent to K-stability with respect to special G-equivariant test configurations. This is furthermore encoded by a single combinatorial condition, checkable in practice. We illustrate on examples and answer along the way a question of Kanemitsu.
Fichier principal
Vignette du fichier
RK1.pdf (229.3 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-03005597 , version 1 (14-11-2020)

Identifiants

  • HAL Id : hal-03005597 , version 1

Citer

Thibaut Delcroix. The Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds. 2020. ⟨hal-03005597⟩
27 Consultations
50 Téléchargements

Partager

Gmail Facebook X LinkedIn More