The Moduli Space of 5 Points on ℙ1 and K3 Surfaces
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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].
KeywordsModuli K3 surfaces quartic del Pezzo surfaces complex ball uniformization
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- [D]I. Dolgachev, Lectures on Invariant Theory, London Math. Soc. Lecture Note Ser., 296, Cambridge 2003.Google Scholar
- [DGK]I. Dolgachev, B. van Geemen, S. Kondō, A complex ball uniformaization of the moduli space of cubic surfaces via periods of K3 surfaces, math.AG/0310342, J. reine angew. Math. (to appear).Google Scholar
- [K2]S. Kondō, The moduli space of curves of genus 4 and Deligne-Mostow’s complex reflection groups, Adv. Studies Pure Math., 36 (2002), Algebraic Geometry 2000, Azumino, 383–400.Google Scholar
- [K3]S. Kondō, The moduli space of 8 points on ℙ1 and automorphic forms, to appear in the Proceedings of the Conference “Algebraic Geometry in the honor of Igor Dolgachev”.Google Scholar
- [Mu]D. Mumford, K. Suominen, Introduction to the theory of moduli, Algebraic Geometry, Oslo 1970, F. Oort, ed., Wolters-Noordholff 1971.Google Scholar
- [N2]V. V. Nikulin, Finite automorphism groups of Kähler K3 surfaces, Trans. Moscow Math. Soc., 38 (1980), 71–135.Google Scholar
- [V]E. B. Vinberg, Some arithmetic discrete groups in Lobachevskii spaces, in “Discrete subgroups of Lie groups and applications to moduli”, Tata-Oxford (1975), 323–348.Google Scholar