New PDF release: Current Topics in Complex Algebraic Geometry

By Herbert Clemens, Janos Kollár

ISBN-10: 0521562449

ISBN-13: 9780521562447

This quantity collects a chain of survey articles on advanced algebraic geometry, which within the early Nineteen Nineties was once present process a massive swap. Algebraic geometry has spread out to rules and connections from different fields that experience generally been far-off. This publication provides a good suggestion of the highbrow content material of the swap of course and branching out witnessed by way of algebraic geometry some time past few years.

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Additional info for Current Topics in Complex Algebraic Geometry

Example text

Let X be a normal variety, and D = KX +B. Let t : X 99 K X be a step (divisorial contraction or flip) in the D-minimal model program. Then a(ν, KX + B ) ≥ a(ν, KX + B) for all valuations ν with small center in X. Also, a(ν, KX + B ) > a(ν, KX + B) if and only if t is not an isomorphism at the center of ν in X. In particular, if KX + B is log terminal (terminal, canonical, log canonical), so is KX + B . Proof. The result is an exercise in the definition if t is a divisorial contraction. 28]. I wish to spend a few words on the meaning of the D-minimal model program.

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Current Topics in Complex Algebraic Geometry by Herbert Clemens, Janos Kollár

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