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H 1 Nonabelian Hodge correspondences for klt varieties and quasi-etale uniformisation

Auteurs : Kebekus, Stefan (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Simpson’s classic nonabelian Hodge correspondence establishes an equivalence of categories between local systems on a projective manifold, and certain Higgs sheaves on that manifold. This talk surveys recent generalisations of Simpson’s correspondence to the context of projective varieties with klt singularities. Perhaps somewhat surprisingly, these spaces exhibit two correspondences: one pertaining to local systems on the whole space, and one to local systems on its smooth locus. As one application, we resolve the quasi-étale uniformisation problem for minimal varieties of general type, and to obtain a complete numerical characterisation of singular quotients of the unit ball by discrete, co-compact groups of automorphisms that act freely in codimension one.

    Keywords : nonabelian Hodge Œtheory; KLT singularities; ball quotients; uniformisation; Higgs sheaves

    Codes MSC :
    14E20 - Coverings
    14E30 - Minimal model program (Mori theory, extremal rays)
    32Q30 - Uniformization
    53C07 - Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
    32Q26 - Notions of stability

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 12/04/2018
      Date de captation : 11/04/2018
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : MP4
      Durée : 00:50:18
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-04-12_Kebekus.mp4

    Informations sur la rencontre

    Nom de la rencontre : French-German meeting on complex algebraic geometry / Rencontre franco-allemande en géométrie algébrique complexe
    Organisateurs de la rencontre : Greb, Daniel ; Höring, Andreas ; Toma, Matei
    Dates : 09/04/2018 - 13/04/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1789.html

    Citation Data

    DOI : 10.24350/CIRM.V.19388203
    Cite this video as: Kebekus, Stefan (2018). Nonabelian Hodge correspondences for klt varieties and quasi-etale uniformisation. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19388203
    URI : http://dx.doi.org/10.24350/CIRM.V.19388203


    Voir aussi

    Bibliographie

    1. Greb, D., Kebekus, S., Peternell, T., & Taji, B. (2018). Harmonic metrics on Higgs sheaves and uniformization of varieties of general type. - https://arxiv.org/abs/1804.01266

    2. Greb, D., Kebekus, S., Peternell, T., & Taji, B. (2017). Nonabelian Hodge Theory for klt spaces and descent theorems for vector bundles. - https://arxiv.org/abs/1711.08159

    3. Greb, D., Kebekus, S., Peternell, T., & Taji, B. (2016). The Miyaoka-Yau inequality and uniformisation of canonical models. < arXiv:1511.08822> - https://arxiv.org/abs/1511.08822

    4. Greb, D., Kebekus, S., & Taji, B. (2016). Uniformisation of higher-dimensional minimal varieties. - https://arxiv.org/abs/1608.06644

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