On the canonical bundle formula for abelian fiber spaces in positive characteristic
A canonical bundle formula is given for \(n+1\) dimensional varieties \(X\) that admit a morphism \(f:X\to C\) onto a curve, such that \(f_*\mathcal{O}_X=\mathcal{O}_C\) and almost all fibers are abelian varieties. Particular interest is given to the question when (and which) multiple of the canonical sheaf yields the structure of the abelian fiber space. In particular, if the characteristic of the base field is zero, \(X\) is a threefold and the Kodaira dimension of \(X\) equals one then \(14K_X\) yields this structure, and this is the optimal value within this class of examples.
scientific article; zbMATH DE number 5895859