Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines

Details Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines

2010-01-27

arxiv.org/abs/1001.4865v2

Mathematics

Algebraic Geometry

42 pages, 2 figures

Scientific paper

In this paper, we give Thomae type formula for \KK surfaces $\cS$ given by double covers of the projective plane branching along six lines. This formula gives relations between theta constants on the bounded symmetric domain of type $I_{22}$ and period integrals of $X$. Moreover, we express the period integrals by using the hypergeometric function $F_S$ of four variables. As an application of our main theorem, we define $\R^4$-valued sequences by mean iterations of four terms, and express their common limits by the hypergeometric function $F_S$.

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