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Licensed Unlicensed Requires Authentication Published by De Gruyter September 27, 2011

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

Keiji Matsumoto and Tomohide Terasoma

Abstract

In this paper, we give a Thomae type formula for K3 surfaces X 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 FS of four variables. As applications of our main theorem, we define ℝ4-valued sequences by mean iterations of four terms, and express their common limits by the hypergeometric function FS.

Received: 2010-04-06
Revised: 2011-04-05
Published Online: 2011-09-27
Published in Print: 2012-08

©[2012] by Walter de Gruyter Berlin Boston