Harmonic metrics on Higgs sheaves and uniformization of varieties of general type
Abstract: We prove a criterion for the existence of harmonic metrics on Higgs bundles that are defined on smooth loci of klt varieties. As one application, we resolve the quasi-étale uniformisation problem for minimal varieties of general type 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. As a further application, we establish a nonabelian Hodge correspondence on smooth loci of klt varieties
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Notes
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Mathematische Annalen. - 378 (2019) , 1061–1094, ISSN: 0025-5831
- Event
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Veröffentlichung
- (where)
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Freiburg
- (who)
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Universität
- (when)
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2020
- Creator
- Contributor
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FRIAS Natur- und Lebenswissenschaften, Medizin und Ingenieurwissenschaften
- DOI
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10.1007/s00208-019-01906-4
- URN
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urn:nbn:de:bsz:25-freidok-1543674
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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25.03.2025, 1:45 PM CET
Data provider
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Associated
- Greb, Daniel
- Kebekus, Stefan
- Peternell, Thomas
- Taji, Behrouz
- FRIAS Natur- und Lebenswissenschaften, Medizin und Ingenieurwissenschaften
- Universität
Time of origin
- 2020
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Tannakian categories of perverse sheaves on abelian varieties
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Equivariant sheaves on flag varieties, DG modules and formality
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Probability sheaves
Higher Sheaves
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Sheaves on manifolds
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