Families of D-minimal models and applications to 3-fold divisorial contractions

Details Families of D-minimal models and applications to 3-fold divisorial contractions Families of D-minimal models and applications to 3-fold divisorial contractions

2002-10-03

arxiv.org/abs/math/0210048v3

Proc. London Math. Soc. (3) 90 (2005), 345-370

Mathematics

Algebraic Geometry

Revised version. A gap in the proofs of Lemma 2.3 and Theorem 2.4 is corrected. 26 pages

Scientific paper

Let X/T be a one parameter family of canonical 3-folds and let D be a Weil divisor on it flat over T. We study the problem of when the D_t-minimal models of X_t form a family and we obtain conditions for this to happen. As an application of this we classify terminal divisorial contractions Y-->X that contract an irreducible divisor E onto a smooth curve C in the case when the general hyperplane section S of X through C is a D5 DuVal singularity.

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