m
     
Multi angle

H 1 Extremal Poincaré type metrics and stability of pairs on Hirzebruch surfaces

Auteurs : Sektnan, Lars Martin (Auteur de la Conférence)
CIRM (Editeur )

    Loading the player...

    Résumé : In this talk I will discuss the existence of complete extremal metrics on the complement of simple normal crossings divisors in compact Kähler manifolds, and stability of pairs, in the toric case. Using constructions of Legendre and Apostolov-Calderbank-Gauduchon, we completely characterize when this holds for Hirzebruch surfaces. In particular, our results show that relative stability of a pair and the existence of extremal Poincaré type/cusp metrics do not coincide. However, stability is equivalent to the existence of a complete extremal metric on the complement of the divisor in our examples. It is the Poincaré type condition on the asymptotics of the extremal metric that fails in general.
    This is joint work with Vestislav Apostolov and Hugues Auvray.

    Keywords : extremal Kähler metrics; toric geometry; complete Poincaré metrics on a complement of divisor

    Codes MSC :
    30F45 - Conformal metrics (hyperbolic, Poincaré, distance functions)
    53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)
    53C55 - Hermitian and Kählerian manifolds (global differential geometry)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 31/01/2018
      Date de captation : 18/01/2018
      Sous collection : Research talks
      Format : MP4
      arXiv category : Differential Geometry ; Algebraic Geometry
      Domaine : Algebraic & Complex Geometry ; Analysis and its Applications
      Durée : 00:49:09
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-01-18_Sektnan.mp4

    Informations sur la rencontre

    Nom de la rencontre : Constant scalar curvature metrics in Kähler and Sasaki geometry / Métriques à courbure scalaire constante en géométrie Kählérienne et Sasakienne
    Organisateurs de la rencontre : Auvray, Hugues ; Huang, Hongnian ; Keller, Julien ; Legendre, Eveline ; Sena-Dias, Rosa
    Dates : 15/01/2018 - 19/01/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1750.html

    Citation Data

    DOI : 10.24350/CIRM.V.19264303
    Cite this video as: Sektnan, Lars Martin (2018). Extremal Poincaré type metrics and stability of pairs on Hirzebruch surfaces. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19264303
    URI : http://dx.doi.org/10.24350/CIRM.V.19264303


    Voir aussi

    Bibliographie

    1. Apostolov, V., Auvray, H., & Sektnan, L.M. (2017). Extremal Kähler Poincaré type metrics on toric varieties. - https://arxiv.org/abs/1711.08424

Titres de périodiques et e-books électroniques (Depuis le CIRM)

Ressources Electroniques

Books & Print journals

Recherche avancée


0
Z