Differential Forms on Log Canonical Spaces
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TLDR
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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Moduli of products of stable varieties
TL;DR: In this paper, the moduli space of a product of stable varieties over the field of complex numbers is studied via the minimal model program, and it is shown that this map is always finite etale.
Journal ArticleDOI
A decomposition theorem for smoothable varieties with trivial canonical class
Stéphane Druel,Henri Guenancia +1 more
TL;DR: In this paper, it was shown that any smoothable complex projective variety admits a finite cover, e.g., in codimension two, with klt singularities and numerically trivial canonical class.
Journal ArticleDOI
Bogomolov-Sommese vanishing on log canonical pairs
TL;DR: Theorem 2 (Bogomolov-Sommese vanishing on lc C-pairs) was proved in this paper, where a C-pair is a pair (X,D) where all the coefficients of D are of the form 1 − 1/n for n ∈ N ∪ {∞}.
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A characterization of finite quotients of Abelian varieties
Steven S. Y. Lu,Behrouz Taji +1 more
TL;DR: In this article, the authors prove a characterization of quotients of Abelian varieties by the actions of finite groups that are free in codimension-one via some vanishing conditions on the orbifold Chern classes.
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Nonabelian Hodge theory for klt spaces and descent theorems for vector bundles
TL;DR: In this article, the authors generalise Simpson's nonabelian Hodge correspondence to the context of projective varieties with Kawamata log terminal (klt) singularities and establish a new restriction theorem for semistable Higgs sheaves defined on the smooth locus of a normal, projective variety.
References
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Daniel Huybrechts,Manfred Lehn +1 more
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TL;DR: In this paper, the authors introduce the minimal model program and the canonical class of rational curves, and present the singularities of the model program, as well as three dimensional flops.
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Existence of minimal models for varieties of log general type
TL;DR: In this paper, it was shown that pl-flips exist in dimension n − 1, assuming finite generation in dimension N − 1 and assuming that pl flips exist in all dimensions.
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Rational Curves on Algebraic Varieties
TL;DR: It is shown here how the model derived recently in [Bouchut-Boyaval, M3AS (23) 2013] can be modified for flows on rugous topographies varying around an inclined plane.