Kodaira's canonical bundle formula and adjunction

If (X,B) is a log canonical pair, it is natural to study the locus nklt(X,B) of points where the pair is not klt. In particular, this chapter proves Kawamata's adjunction formula: if W is an irreducible subvariety of nklt(X,B), then the restriction of K+B to W is expressed naturally in terms of the canonical class of W. This topic provides a simultaneous generalization of the classical adjunction formula, the formula for the canonical class of a smooth blow up, and Kodaira's formula for the canonical class of a relatively minimal elliptic surface. The ideas have many applications in higher dimensional algebraic geometry.