${\bar{\mathbf{C}}}_{\mathbf{n},\mathbf{n}-\mathbf{1}}$ revisited

The main purpose of this paper is to make ${\bar{C}}_{n,n-1}$, which is the main theorem of [Ka1] Y.Kawamata, Addition formula of logarithmic Kodaira dimensions for morphisms of relative dimension one, more accessible.