Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Takeshi Sasaki and Masaaki Yoshida

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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 $E_6$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 75, Number 7 (1999), 129-133.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393866

Digital Object Identifier
doi:10.3792/pjaa.75.129

Mathematical Reviews number (MathSciNet)
MR1729861

Zentralblatt MATH identifier
0976.33013

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

Citation

Sasaki, Takeshi; Yoshida, Masaaki. 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 (1999), no. 7, 129--133. doi:10.3792/pjaa.75.129. https://projecteuclid.org/euclid.pja/1148393866


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References

  • D. Allcock, J. Carlson and D. Toledo: A complex hyperbolic structure for moduli of cubic surfaces. C. R. Acad. Sci., 326, 49–54 (1998).
  • J. Carlson and D. Toledo: Discriminant compliments and kernels of monodromy representations, alg-geom/9708002, version 3, 11 May 1998.
  • I. Naruki: Cross ratio variety as a moduli space of cubic surfaces. Proc. London Math. Soc., 45, 1–30 (1982).
  • T. Sasaki and M. Yoshida: Linear differential equations in two variables of rank 4, I, II. Math. Ann., 282, 69–93, 95–111 (1988).
  • J. Sekiguchi and M. Yoshida: $W(E_6)$-orbits of the configurations space of 6 lines on the real projective space. Kyushu J. Math., 51, 1–58 (1997).
  • M. Yoshida: The real loci of the configuration space of six points on the projective line and a Picard modular 3-fold. Kumamoto J. Math., 11, 43–67 (1998).
  • M. Yoshida: Fuchsian Differential Equations. Vieweg Verlag, Wiesbaden, pp. 1–215 (1987).
  • M. Yoshida: Hypergeometric Functions, My Love. Vieweg Verlag, Wiesbaden, pp. 1–292 (1997).