On explicit birational geometry for minimal n-folds of canonical dimension n − 1

Let (Formula presented.) be any integer. We study the optimal lower bound of the canonical volume and the optimal upper bound of the canonical stability index for minimal projective (Formula presented.) -folds of general type, which are canonically fibered by (Formula presented.) -folds ((Formula presented.)). The results for (Formula presented.) are known to experts. In this article, we compute sharp bounds for (Formula presented.) and give some characterization of optimal examples. The machinery introduced is applicable to all canonical dimensions (Formula presented.).