# Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines - Mathematics > Algebraic Geometry

Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

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

Author: ** Keiji Matsumoto, Tomohide Terasoma**

Source: https://arxiv.org/