Analytic rigidity of K-trivial extremal contractions of smooth 3-folds

Details Analytic rigidity of K-trivial extremal contractions of smooth 3-folds Analytic rigidity of K-trivial extremal contractions of smooth 3-folds

2002-04-01

arxiv.org/abs/math/0204015v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

We discuss the problem of classifying birational extremal contractions of smooth threefolds where the canonical bundle is trivial along the curves contracted, in the case when a divisor is contracted to a point. We prove the analytic rigidity of the contraction in the case this divisor is normal of degree >= 5 (i.e. we show that the analytic structure of the contraction is completely determined by the isomorphism class of the exceptional locus and its normal bundle in X). This was previously known only in the case of smooth exceptional locus.

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