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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Families over special base manifolds and a conjecture of Campana
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Families over special base manifolds and a conjecture of Campana
Kelly Jabbusch,Stefan Kebekus +1 more
TL;DR: In this article, it was shown that the Bogomolov-Sommese vanishing theorem is not necessarily isotrivial when Y is a surface or threefold, using sheaves of symmetric differentials associated to fractional boundary divisors on log canonical spaces.
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Codimension 1 foliations with numerically trivial canonical class on singular spaces
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Moduli of products of stable varieties
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References
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Basic Algebraic Geometry
TL;DR: The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds as discussed by the authors, and is suitable for beginning graduate students.
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The geometry of moduli spaces of sheaves
Daniel Huybrechts,Manfred Lehn +1 more
TL;DR: In this paper, the Grauert-Mullich Theorem is used to define a moduli space for sheaves on K-3 surfaces, and the restriction of sheaves to curves is discussed.
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Birational Geometry of Algebraic Varieties
János Kollár,Shigefumi Mori +1 more
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.