Discrete-torsion conjecture for multiple fibers of Calabi–Yau genus-one fibrations

Let a Calabi–Yau variety admit a relatively minimal genus-one fibration with multiple fibers, and let a multiple fiber have multiplicity $m$. Discrete-torsion conjecture. The multiple fibers of multiplicity $m$ are associated with discrete torsion $\mathbb{Z}/m\mathbb{Z}$. This is proposed alongside an extension of Kodaira classification to birationally equivalent relatively minimal genus-one fibered varieties; the supplied text cites recent work suggesting the association but does not resolve it in general.