Existence of minimal models for varieties of log general type
TLDR
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.Abstract:
Assuming finite generation in dimension n − 1, we prove that pl-flips exist in dimension n.read more
Citations
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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.
Book
Analytic Methods in Algebraic Geometry
TL;DR: In this paper, the authors describe analytic techniques useful in the study of questions pertaining to linear series, multiplier ideals, and vanishing theorems for algebraic vector bundles, assuming that the reader is already somewhat acquainted with the basic concepts of sheaf theory, homological algebra, and complex differential geometry.
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Convex Bodies Associated to Linear Series
Robert Lazarsfeld,Mircea Mustata +1 more
TL;DR: In this article, it was shown that the log-concavity of multiplicities can be constructed for an arbitrary big divisor in convex geometry, and that the construction goes through for the case of infinite divisors.
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Fundamental Theorems for the Log Minimal Model Program
TL;DR: In this article, the authors proved the cone theorem and the contraction theorem for pairs (X;B), where X is a normal variety and B is an effective R-Divisor on X such that KX + B is R-Cartier.
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Canonical measures and Kähler-Ricci flow
Jian Song,Gang Tian +1 more
TL;DR: In this paper, it was shown that the Kahler-Ricci flow on an algebraic manifold of positive Kodaira dimension and semi-ample canonical line bundle converges to a unique canonical metric on its canonical model.
References
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I and i
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
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The irreducibility of the space of curves of given genus
Pierre Deligne,David Mumford +1 more
TL;DR: In this article, the authors implique l'accord avec les conditions generales d'utilisation (http://www.numdam.org/legal.php).
Book
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.