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Positivity of the Moduli Part.
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In this article, it was shown that termination of flips implies the b-nefness of the moduli part of a log canonical pair with respect to a contraction, generalising the case of trivial fibrations.Abstract:
We prove the Cone Theorem for algebraically integrable foliations. As a consequence, we show that termination of flips implies the b-nefness of the moduli part of a log canonical pair with respect to a contraction, generalising the case of lc trivial fibrations.read more
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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.
Journal ArticleDOI
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.
Journal ArticleDOI
Rational connectedness and boundedness of Fano manifolds
Journal ArticleDOI
Subadjunction of log canonical divisors, II
TL;DR: In this paper, a subadjunction formula of log canonical divisors is extended to the case when the codimension of the minimal center is arbitrary by using the positivity of the Hodge bundles.
Journal ArticleDOI
Towards the second main theorem on complements
TL;DR: In this article, the boundedness of complements modulo two conjectures, Borisov-Alexeev conjecture and effective adjunction for fibre spaces, was proved and proved in two particular cases.