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

• Autores: Nikolaos Tziolas
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 90, Nº 2, 2005, págs. 345-370
• Idioma: inglés
• DOI: 10.1112/s002461150401514x
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• Resumen

  • 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.