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

2010/01/27 by Keiji Matsumoto, Matsumoto, Keiji, Tomohide Terasoma +1
Mathematics · #11F55 #33C70 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:11F55 #msc:33C70

paper · pdf · doi:10.48550/arxiv.1001.4865

42 pages, 2 figures

arxiv created 2010/02/03 · arxiv updated 2010/02/26

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 I₂₂ 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 \R⁴-valued sequences by mean iterations of four terms, and express their common limits by the hypergeometric function F_S.

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