The uniformizing differential equation of the complex hyperbolic structure on the moduli space of marked cubic surfaces

Takeshi Sasaki; Masaaki Yoshida

doi:10.3792/pjaa.75.129

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Sept. 1999 The uniformizing differential equation of the complex hyperbolic structure on the moduli space of marked cubic surfaces

Takeshi Sasaki, Masaaki Yoshida

Proc. Japan Acad. Ser. A Math. Sci. 75(7): 129-133 (Sept. 1999). DOI: 10.3792/pjaa.75.129

Abstract

We find the uniformizing equation, governing the developing map, of a complex hyperbolic structure on the (4-dimensional) moduli space of marked cubic surfaces. Our equation is invariant under the action of the Weyl group of type $E_6$.

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Takeshi Sasaki. Masaaki Yoshida. "The uniformizing differential equation of the complex hyperbolic structure on the moduli space of marked cubic surfaces." Proc. Japan Acad. Ser. A Math. Sci. 75 (7) 129 - 133, Sept. 1999. https://doi.org/10.3792/pjaa.75.129

Information

Published: Sept. 1999

First available in Project Euclid: 23 May 2006

zbMATH: 0976.33013

MathSciNet: MR1729861

Digital Object Identifier: 10.3792/pjaa.75.129

Keywords: complex hyperbolic structure , cubic surface , developing map , moduli space , Schwarzian derivative , uniformizing differential equation , Weyl group