\(\mathrm{klt}\) varieties with trivial canonical class: holonomy, differential forms, and fundamental groups

DOI10.2140/gt.2019.23.2051zbMath1423.14110arXiv1704.01408OpenAlexW3101489534WikidataQ115231038 ScholiaQ115231038MaRDI QIDQ2318712

Daniel Greb, Henri Guenancia, Stefan Kebekus

Publication date: 16 August 2019

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.01408

zbMATH Keywords

stabilitydifferential formsfundamental groupsCalabi-Yau varietiesKähler-Einstein metricsirreducible holomorphic symplectic varietiesBochner principlesingular Beauville-Bogmolov decomposition

Mathematics Subject Classification ID

Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Minimal model program (Mori theory, extremal rays) (14E30) Compact Kähler manifolds: generalizations, classification (32J27)

Related Items (25)

Algebraicity of foliations on complex projective manifolds, applications ⋮ Algebraic approximation and the decomposition theorem for Kähler Calabi-Yau varieties ⋮ Free abelian group actions on normal projective varieties: submaximal dynamical rank case ⋮ Codimension \(1\) foliations with numerically trivial canonical class on singular spaces ⋮ The global moduli theory of symplectic varieties ⋮ A global Torelli theorem for singular symplectic varieties ⋮ Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities ⋮ Rational curves on genus-one fibrations ⋮ On generalised abundance. I ⋮ Kähler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups ⋮ Algebraic integrability of foliations with numerically trivial canonical bundle ⋮ The second integral cohomology of moduli spaces of sheaves on K3 and abelian surfaces ⋮ Open problems on structure of positively curved projective varieties ⋮ The nonvanishing problem for varieties with nef anticanonical bundle ⋮ A Bochner principle and its applications to Fujiki class 𝒞 manifolds with vanishing first Chern class ⋮ Birational boundedness of rationally connected Calabi-Yau 3-folds ⋮ Examples of Irreducible Symplectic Varieties ⋮ On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four ⋮ Rational curves on fibered varieties ⋮ Holomorphic \(\operatorname{GL}_2(\mathbb{C})\)-geometry on compact complex manifolds ⋮ THE INTEGRAL HODGE CONJECTURE FOR 3-FOLDS OF KODAIRA DIMENSION ZERO ⋮ The Bogomolov-Beauville-Yau decomposition for klt projective varieties with trivial first Chern class - without tears ⋮ Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities ⋮ On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties ⋮ Orbifold stability and Miyaoka-Yau inequality for minimal pairs

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