Kodaira dimension
Given the conjectures mentioned, the classification of algebraic varieties would largely reduce to the cases of Kodaira dimension formula_5, 0 and general type. For Kodaira dimension formula_5 and 0, there are some approaches to classification. The minimal model and abundance conjectures would imply that every variety of Kodaira dimension formula_5 is uniruled, and it is known that every uniruled variety in characteristic zero is birational to a Fano fiber space. The minimal model and abundance conjectures would imply that every variety of Kodaira dimension 0 is birational to a Calabi-Yau variety with terminal singularities.