English
Nonabelian Hodge correspondences for klt varieties and quasi-etale uniformisation
Multi angle
Auteurs : Kebekus, Stefan (Auteur de la conférence)
CIRM (Editeur )
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
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.
Mots-Clés : nonabelian Hodge theory; KLT singularities; ball quotients; uniformisation; Higgs sheaves
Codes MSC : Mots-Clés : nonabelian Hodge theory; KLT singularities; ball quotients; uniformisation; Higgs sheaves
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
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 12/04/2018 Date de Captation : 11/04/2018 Collection : Exposés de recherche Sous Collection : Research talks Catégorie arXiv : Algebraic Geometry ; Complex Variables ; Differential Geometry Domaine(s) : Géométrie Complexe & géométrie Algébrique Format : MP4 (.mp4) - HD Durée : 00:50:18 Audience : Chercheurs Download : https://videos.cirm-math.fr/2018-04-12_Kebekus.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : French-German meeting on complex algebraic geometry / Rencontre franco-allemande en géométrie algébrique complexeOrganisateurs de la Rencontre : Greb, Daniel ; Höring, Andreas ; Toma, Matei Dates : 09/04/2018 - 13/04/2018 Année de la rencontre : 2018 URL de la Rencontre : https://conferences.cirm-math.fr/1789.html
Données de citation
DOI : 10.24350/CIRM.V.19388203Citer cette vidéo: 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 |
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Bibliographie
- Greb, D., Kebekus, S., Peternell, T., & Taji, B. (2018). Harmonic metrics on Higgs sheaves and uniformization of varieties of general type.
- Greb, D., Kebekus, S., Peternell, T., & Taji, B. (2017). Nonabelian Hodge Theory for klt spaces and descent theorems for vector bundles.
- 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
- Greb, D., Kebekus, S., & Taji, B. (2016). Uniformisation of higher-dimensional minimal varieties.
