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Nonabelian Hodge correspondences for klt varieties and quasi-etale uniformisation
Multi angle
Authors : Kebekus, Stefan (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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 theory; KLT singularities; ball quotients; uniformisation; Higgs sheaves
MSC Codes : Keywords : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 12/04/2018 Conference Date : 11/04/2018 Subseries : Research talks arXiv category : Algebraic Geometry ; Complex Variables ; Differential Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:50:18 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-04-12_Kebekus.mp4 
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Information on the Event
Event Title : French-German meeting on complex algebraic geometry / Rencontre franco-allemande en géométrie algébrique complexeEvent Organizers : Greb, Daniel ; Höring, Andreas ; Toma, Matei Dates : 09/04/2018 - 13/04/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1789.html
Citation Data
DOI : 10.24350/CIRM.V.19388203Cite 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 |
See Also
- [Multi angle] Gonality and zero-cycles of abelian varieties / Author of the conference Voisin, Claire.
- [Multi angle] Signature morphisms from the Cremona group / Author of the conference Zimmermann, Susanna.
- [Multi angle] Improved bounds for the Kobayashi conjecture on generic hyperbolicity / Author of the conference Demailly, Jean-Pierre.
- [Post-edited] Periods of polarized hyperkähler manifolds / Author of the conference Debarre, Olivier.
- [Multi angle] Deformation theory of twistor spaces of K3 surfaces / Author of the conference Brecan, Ana-Maria.
Bibliography
- 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.
