Subadjunction of log canonical divisors II

Abstract. We extend a subadjunction formula of log canonical divisors as in [Kawamata, Contemp. Math. 207 (1997), 79–88] to the case when the codimension of the minimal center is arbitrary by using the positivity of the Hodge bundles. 1. Main result. The canonical divisor KX of a variety X is essentially the only divisor naturally attached to X up to the linear equivalence. The log canonical divisor KX + D is its generalization for the pair (X, D) consisting of a variety and a divisor on it. The adunction formula expresses the relationship between (log) canonical divisors of varieties which are related by a morphism f: X! Y. For example, if X is a smooth divisor on a smooth variety Y, then the adjunction formula says that (KY +X)jX = KX. If Y is singular, then an additional positive term may appear on the right-hand side, so that the formula is called a subadjunction formula. Kodaira’s canonical bundle formula for an elliptic surface f: X! Y is another example. The moduli of the fibers of f has a positive contribution to KX; this is another example of the positivity. For a general fiber space, we proved a semipositivity theorem in [K1] by usin