Differential Forms on Log Canonical Spaces
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In this paper, it was shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities.Abstract:
The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.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.
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Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs
TL;DR: In this article, it was shown that the Yau-Tian-Donaldson conjecture holds in the case of (possibly singular) canonically polarized (or quasi-projective) varieties.
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\'Etale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties
TL;DR: In this article, it was shown that for a quasi-projective variety X with only Kawamata log terminal singularities, there exists a Galois cover (GCC) ramified only over the singularities of X, such that the etale fundamental groups of X and Y agree.
Journal ArticleDOI
Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of abelian varieties
TL;DR: In this paper, it was shown that for a quasiprojective variety X with only Kawamata log terminal singularities, there exists a Galois cover Y→X, ramified only over the singularities of X, such that the etale fundamental groups of Y and of Yreg agree.
Journal ArticleDOI
A decomposition theorem for singular spaces with trivial canonical class of dimension at most five
TL;DR: 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.
References
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