A decomposition theorem for singular spaces with trivial canonical class of dimension at most five
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In this article, the authors extend the Beauville-Bogomolov decomposition theorem to the singular setting and show that any complex projective variety of dimension at most five with canonical singularities and numerically trivial canonical class admits a finite cover, etale in codimension one, that decomposes as a product of an Abelian variety.Abstract:
In this paper we partly extend the Beauville–Bogomolov decomposition theorem to the singular setting. We show that any complex projective variety of dimension at most five with canonical singularities and numerically trivial canonical class admits a finite cover, etale in codimension one, that decomposes as a product of an Abelian variety, and singular analogues of irreducible Calabi–Yau and irreducible holomorphic symplectic varieties.read more
Citations
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Algebraic integrability of foliations with numerically trivial canonical bundle
Andreas Höring,Thomas Peternell +1 more
TL;DR: In this article, the flatness of leaves for sufficiently stable foliations with numerically trivial canonical bundles was proved under certain stability conditions, which implies the algebraicity of leaves in the case of minimal models with trivial canonical class.
Journal ArticleDOI
Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups
TL;DR: In this paper, the authors investigated the holonomy group of singular Kahler-Einstein metrics on klt varieties with numerically trivial canonical divisor, and showed that up to finite quasi-etale covers, the varieties with strongly stable tangent sheaves are either Calabi-Yau or irreducible holomorphic symplectic.
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The global moduli theory of symplectic varieties
Benjamin Bakker,Christian Lehn +1 more
TL;DR: In this article, the authors develop the global moduli theory of symplectic varieties and prove a number of analogs of classical results from the smooth case, including a global Torelli theorem, which does not use the existence of a hyperkahler metric or twistor deformations.
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A global Torelli theorem for singular symplectic varieties
Benjamin Bakker,Christian Lehn +1 more
TL;DR: In this article, the moduli theory of symplectic varieties admits a resolution by an irreducible symplectic manifold, and an analog of Verbitsky's global Torelli theorem for the locally trivial deformations of such varieties is proved.
Journal ArticleDOI
Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities
Stefan Kebekus,Christian Schnell +1 more
TL;DR: In this article, the authors investigated under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities, and gave a simple necessary and sufficient condition for this, whose proof relies on the Decomposition Theorem and Saito's theory of mixed Hodge modules.
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