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

DOI10.1515/CRELLE.2011.144zbMATH Open1251.14028arXiv1001.4865OpenAlexW2074303127MaRDI QIDQ2910997

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Publication date: 12 September 2012

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Abstract: 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 $F_S$.

Full work available at URL: https://arxiv.org/abs/1001.4865

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