\#-minimal models of uniruled 3-folds
Let \(T\) be a terminal \(\mathbb{Q}\)-factorial uniruled 3-fold and let \(\mathbf H\) be a nef movable linear system on \(T\). According to \textit{M. Reid} [Math. Ann. 275, 71--80 (1986; Zbl 0579.14017)], a \(\#\)-minimal model of the pair \((T, {\mathbf H})\) is a suitable pair \((T^{\#}, {\mathbf H}^{\#})\) such that there is a birational map \(\phi: T\to T^{\#}\) with \(\phi_*{\mathbf H}= {\mathbf H}^{\#}\). In this paper, the author proves the existence of \(\#\)-minimal models and he classifies them when \(\mathbf H\) is nef and big and the generic \(H\in{\mathbf H}\) is a smooth surface of negative Kodaira dimension. Moreover, he lists all possible \(\#\)-minimal models of small degree 3-folds embedded in projective spaces.
scientific article; zbMATH DE number 2075749