Arakelov inequality for families of pairs

Abstract

We establish an Arakelov-type inequality for a morphism $f \colon (X,Δ) \to S$, where $(X,Δ)$ is a simple normal crossing semi-log canonical pair and $S$ is a smooth projective variety. As a consequence, we derive a bound on the Iitaka volumes of algebraic fiber spaces whose geometric generic fiber admits a good minimal model.