Families of K3 surfaces over curves satisfying the equality of Arakelov-Yau's type and modularity

Xiaotao Sun, Sheng-Li Tan, Kang Zuo

Let $f:X\to C$ be a family of semistable K3 surfaces with non-empty set $S$ of singular fibres having infinite local monodromy. Then, when the so called Arakelov-Yau inequality rea…