# On a canonical bundle formula on a Calabi-Yau type variety

Let $$(X,B)$$ be a Calabi-Yau pair, that is, $$(X,B)$$ is lc (or klt for simplicity) and $$K_X+B \sim_\mathbb{Q} 0$$. Given a fibration $$f:X \to Y$$, there is an induced generalised pair $$(Y,B_Y+M_Y)$$ with $$B_Y$$ the discriminant part and $$M_Y$$ the moduli part. Do we know any information about $$M_Y$$ other than it is b-nef and abundant? Is there an easy example that $$M_Y \nsim_\mathbb{Q} 0$$?

• Have you looked at Ambro's "Shokurov’s Boundary Property" (J.Diff Geom, 2004)? He gives an example on the first page which may be interesting to you. Jun 26, 2019 at 19:34