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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N-R2] , 2θ-linear systems on Abelian varieties, Vector bundles on algebraic varieties, Oxford University Press, 1987, pp. 415–427. [N-Rs] M. S. Narasimhan and T. R. Ramadas, Factorization of generalized Theta functions I, Invent. Math. 114 (1993), 565–623. [LP] J. Le Potier, Module des fibr´ es semi-stables et fonctions thˆ eta, preprint (1993). [R] M. Raynaud, Sections des fibr´ es vectoriels sur une courbe, Bull. Soc. Math. France 110 (1982), 103–125. [S] A. Szenes, The combinatorics of the Verlinde formula, preprint (1994).

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

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