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

Published online by Cambridge University Press:  25 February 2005

Nikolaos Tziolas
Nikolaos Tziolas
Affiliation:
Max Planck Institute für Mathematik, Vivatsgasse 7, Bonn 53111, Germany. E-mail: tziolas@mpim-bonn.mpg.de Current address:, Department of Mathematics, University of Crete, Knossos Avenue, Heraklion 71409, Greece. E-mail: tziolas@math.uoc.gr
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Abstract

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 $E \subset Y \leftarrow C \subset X$ contracting an irreducible surface $E$ onto the smooth curve $C$, in the case when the general section of $X$ through $C$ is a $D_5$ DuVal singularity.

Keywords

14E30 (primary)14E35 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 90 , Issue 2 , March 2005 , pp. 345 - 370
Copyright
2005 London Mathematical Society

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