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On the classification of crepant analytically extremal contractions of smooth three-folds

Published online by Cambridge University Press:  15 October 2004

Csilla Tamás
Csilla Tamás
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602-7403, USActamas@math.uga.edu
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Abstract

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We discuss the problem of classifying crepant analytically extremal contractions $X \to Y$ from a smooth 3-fold, contracting an irreducible normal divisor D in X to a point P in Y. We prove that, if D has degree $(-K_D)^2 \geq 5$, the analytic structure of the contraction is completely determined by the isomorphism class of the exceptional locus and its normal bundle. This was previously known only for a smooth exceptional locus D.

Keywords

3-foldsbirationalcrepantextremalcontractionsclassificationdel Pezzo surfaces14E0514J30 (primary)14E3014B10 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 6 , November 2004 , pp. 1561 - 1578
Copyright
Foundation Compositio Mathematica 2004