Canonical bundle formula and base change

Abstract

We study invariants of an elliptic fibration over a complete discrete valuation ring with algebraically closed residue field. The invariants are given by the relative dualizing sheaf and the first direct image sheaf of the structure sheaf. In the studies of an elliptic surface over an algebraically closed field, the invariants appear as local invariants that determine important global invariants such as its plurigenera. We determine the invariants by investigating the change of the invariants by base change.