Nonabelian Hodge theory for klt spaces and descent theorems for vector bundles

DOI10.1112/S0010437X18007923zbMath1443.14009arXiv1711.08159WikidataQ128429175 ScholiaQ128429175MaRDI QIDQ5212322

Daniel Greb, Stefan Kebekus, Behrouz Taji, Thomas Peternell

Publication date: 28 January 2020

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.08159

zbMATH Keywords

klt singularitiesnonabelian Hodge theorydescent criteria for vector bundles

Mathematics Subject Classification ID

Complex-analytic moduli problems (32G13) Period matrices, variation of Hodge structure; degenerations (32G20) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Variation of Hodge structures (algebro-geometric aspects) (14D07) Minimal model program (Mori theory, extremal rays) (14E30) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

Related Items (6)

Nonabelian Hodge theory for Fujiki class 𝒞 manifolds ⋮ Non-abelian Hodge theory and related topics ⋮ Harmonic metrics on Higgs sheaves and uniformization of varieties of general type ⋮ Projectively flat klt varieties ⋮ Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities ⋮ Numerical characterization of some toric fiber bundles

Cites Work

• Simultaneous normalization and algebra husks
• An optimal extension theorem for 1-forms and the Lipman-Zariski conjecture
• On codimension 1 del Pezzo foliations on varieties with mild singularities
• Differential forms on log canonical spaces
• Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of abelian varieties
• Stable reflexive sheaves
• Higgs bundles and local systems
• The adjunction theory of complex projective varieties
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
• Mori contractions of maximal length
• Bogomolov's inequality for Higgs sheaves in positive characteristic
• Orbifold stability and Miyaoka-Yau inequality for minimal pairs
• Harmonic metrics on Higgs sheaves and uniformization of varieties of general type
• On Shokurov's rational connectedness conjecture
• Pull-back morphisms for reflexive differential forms
• Semistability vs. nefness for (Higgs) vector bundles
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Troisième partie). Rédigé avec la colloboration de J. Dieudonné
• Representations lineaires et compactification profinie des groups discrets
• Equations différentielles à points singuliers réguliers
• Harmonic Bundles on Noncompact Curves
• Asymptotic behaviour of tame harmonic bundles and an application to pure twistor 𝐷-modules. I
• Asymptotic behaviour of tame harmonic bundles and an application to pure twistor 𝐷-modules. II
• Existence of minimal models for varieties of log general type
• Local Simple Connectedness of Resolutions of Log-Terminal Singularities
• The Miyaoka-Yau inequality and uniformisation of canonical models
• Uniformisation of higher-dimensional minimal varieties
• Wild Hodge theory and Hitchin-Kobayashi correspondence [after T. Mochizuki]
• Profinite Groups
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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