Period map of triple coverings of ${\mathbf{P}}^2$ and mixed Hodge structures

We study a period map for triple coverings of ${\mathbf{P}}^2$branching along special configurations of $6$ lines. Though the moduli space of special configurations isa two dimensional variety,the minimal models of the coverings form a oneparameter family of K3 surfaces.We extract extra one dimensionalinformation from the mixed Hodge structure on the second relative homology group.