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February 2018 The Fermat septic and the Klein quartic as moduli spaces of hypergeometric Jacobians
Kenji KOIKE
Hokkaido Math. J. 47(1): 109-141 (February 2018). DOI: 10.14492/hokmj/1520928062

Abstract

We study the Schwarz triangle function with the monodromy group $\Delta(7,7,7)$, and we construct its inverse by theta constants. As consequences, we give uniformizations of the Klein quartic curve and the Fermat septic curve as Shimura curves parametrizing Abelian $6$-folds with endomorphisms $\mathbb{Z}[\zeta_7]$.

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Kenji KOIKE. "The Fermat septic and the Klein quartic as moduli spaces of hypergeometric Jacobians." Hokkaido Math. J. 47 (1) 109 - 141, February 2018. https://doi.org/10.14492/hokmj/1520928062

Information

Published: February 2018
First available in Project Euclid: 13 March 2018

zbMATH: 06853593
MathSciNet: MR3773727
Digital Object Identifier: 10.14492/hokmj/1520928062

Subjects:
Primary: 14G35, 30F10, 33C05

Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

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Vol.47 • No. 1 • February 2018
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