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The Moduli Space of 5 Points on ℙ1 and K3 Surfaces

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Arithmetic and Geometry Around Hypergeometric Functions

Part of the book series: Progress in Mathematics ((PM,volume 260))

Abstract

We show that the moduli space of 5 ordered points on ℙ1 is isomorphic to an arithmetic quotient of a complex ball by using the theory of periods of K3 surfaces. We also discuss a relation between our uniformization and the one given by Shimura [S], Terada [Te], Deligne-Mostow [DM].

Research of the author is partially supported by Grant-in-Aid for Scientific Research A-14204001, Japan.

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Author information

Authors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan

    Shigeyuki Kondō

Authors
  1. Shigeyuki Kondō
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099, Berlin

    Rolf-Peter Holzapfel

  2. Department of Mathematics, Galatasaray University, 34357, Besiktas, Istanbul, Turkey

    A. Muhammed Uludağ

  3. Department of Mathematics, Kyushu University, Fukuoka, 810-8560, Japan

    Masaaki Yoshida

Additional information

Dedicated to Professor Yukihiko Namikawa on his 60th birthday

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Kondō, S. (2007). The Moduli Space of 5 Points on ℙ1 and K3 Surfaces. In: Holzapfel, RP., Uludağ, A.M., Yoshida, M. (eds) Arithmetic and Geometry Around Hypergeometric Functions. Progress in Mathematics, vol 260. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8284-1_7

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