Log canonical pairs over varieties with maximal Albanese dimension

Abstract

Let $(X,B)$ be a log canonical pair over a normal variety $Z$ with maximal Albanese dimension. If $K_X+B$ is relatively abundant over $Z$ (for example, $K_X+B$ is relatively big over $Z$), then we prove that $K_X+B$ is abundant. In particular, the subadditvity of Kodaira dimensions $\kappa (K_X+B)\ge \kappa (K_F+B_F)+\kappa (Z)$ holds, where $F$ is a general fiber, $K_F+B_F=(K_X+B){|}_F$, and $\kappa (Z)$ means the Kodaira dimension of a smooth model of $Z$. We discuss several variants of this result in Section 4. We also give a remark on the log Iitaka conjecture for log canonical pairs in Section 5.

arXiv comment24 pages. Some typos fixed

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