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

Nikolaos Tziolas

• 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.