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We study a period map for triple coverings of $\mathbf P^2$branching alongspecial configurations of $6$ lines. Though the moduli space of specialconfigurations isa two dimensional variety,the minimal models of the coveringsform a oneparameter family of K3 surfaces.We extract extra onedimensionalinformation from the mixed Hodge structure on the second relativehomology group.

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