Period Map of Triple Coverings of P and Mixed Hodge Structures

  • Keiji Matsumoto

    Hokkaido University, Sapporo, Japan
  • Tomohide Terasoma

    Hosei University, Tokyo, Japan
Period Map of Triple Coverings of P$^2$ and Mixed Hodge Structures cover

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Abstract

We study a period map for triple coverings of branching along special configurations of 6 lines. Though the moduli space of special configurations is a two-dimensional variety, the minimal models of the coverings form a one-parameter family of K3 surfaces. We extract extra one-dimensional information from the mixed Hodge structure on the second relative homology group. We define the period map from the moduli space of marked configurations to the domain , where is the right half-plane, and give a defining equation of its image by a theta function. We write down the inverse of the period map using theta functions.

Cite this article

Keiji Matsumoto, Tomohide Terasoma, Period Map of Triple Coverings of P and Mixed Hodge Structures. Publ. Res. Inst. Math. Sci. 55 (2019), no. 3, pp. 489–529

DOI 10.4171/PRIMS/55-3-2