Journal ArticleDOI
BIRATIONAL GEOMETRY OF ALGEBRAIC VARIETIES (Cambridge Tracts in Mathematics 134)
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This article is published in Bulletin of The London Mathematical Society.The article was published on 2000-01-01. It has received 651 citations till now. The article focuses on the topics: Minimal model program & Birational geometry.read more
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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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Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory
TL;DR: In this article, the authors theoretically compare the Bayes cross-validation loss and the widely applicable information criterion and prove two theorems: 1) The Bayes generalization error is asymptotically equal to 2λ/n, where λ is the real log canonical threshold and n is the number of training samples.
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Monge-Ampère equations in big cohomology classes
TL;DR: In this paper, the authors define non-pluripolar products of an arbitrary number of closed positive (1, 1)-currents on a compact Kahler manifold X and show that the solution has minimal singularities in the sense of Demailly if μ has L 1+e-density with respect to Lebesgue measure.
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Boundedness of pluricanonical maps of varieties of general type
TL;DR: In this article, it was shown that certain log forms may be lifted from a divisor to the ambient variety of a smooth projective variety of general type and dimension n.
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On Shokurov's rational connectedness conjecture
TL;DR: In this article, it was shown that the fibres of a resolution of a variety with divisorial log terminal singularities are rationally chain connected, which is the same as the rational connectedness conjecture of Shokurov.