Tohoku Mathematical Journal
2022
March
SECOND SERIES VOL. 74, NO. 1

Tohoku Math. J.
74 (2022), 109-149

Title SCHWARZ'S MAP FOR APPELL'S SECOND HYPERGEOMETRIC SYSTEM WITH QUARTER INTEGER PARAMETERS

Author Keiji Matsumoto, Shohei Osafune and Tomohide Terasoma

(Received July 27, 2020, revised December 3, 2020)
Abstract. We study Schwarz's map for Appell's second system ${\mathcal F}_2$ of hypergeometric differential equations in two variables with parameters $a=c_1=c_2=\frac{1}{2}$, $b_1=b_2=\frac{1}{4}$. By using theta functions with characteristics, we give a defining equation of an analytic set in ${\mathbb C}^2\times {\mathbb H}$ of its image, and express its inverse.

Mathematics Subject Classification. Primary 14H42; Secondary 14H40, 32G20, 33C65.
Key words and phrases. Schwarz's map, Appell's second hypergeometric system, theta function, Prym variety.

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