Threefolds with Kodaira Dimension 0 or 3

Stagnaro, Ezio

Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 1149-1182

Résumé

Using the theory of adjoints and pluricanonical adjoints, we construct three nonsingular threefolds, as desingularizations of degree six hypersurfaces in $\mathbb{P}^4$, having the irregularities $q_1=q_2= 0$ and the following periodical sequences of plurigenera respectively \begin{equation*}(p_g,P_2, P_3, \ldots, P_m, \ldots) = (0, 0, 1, 0, 0, 1,\ldots),(0, 0, 0, 1, 0, 0, 0, 1, \ldots), (0, 0, 0, 0, 1, 0, 0, 0, 0, 1, \ldots).\end{equation*}In the Appendix, starting from the second above-mentioned example, we construct a threefold of general type with $qq_1 = q_2 = 0, p_g =1$, $P_2=2$ whose m-canonical transformation is birational if and only if $m \geq 11$.