The moduli space of 5 points on P¹ and K3 surfaces

2005/07/01 by Shigeyuki Kondo, Kondo, Shigeyuki · 1 citation
Mathematics · #14J10 #14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J10 #msc:14J28

paper · pdf · doi:10.48550/arxiv.math/0507006

15 pages

arxiv created 2005/07/01 · arxiv updated 2009/12/01

Abstract

We show that the moduli space of ordered 5 points on the projective line 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, Terada and Deligne-Mostow.

Cited by

• Remarks on two problems by Hassett

Related

• The moduli space of 8 points on \bf P¹ and automorphic forms
• Moduli spaces of K3 surfaces and complex ball quotients
• A Complex Ball Uniformization of the Moduli Space of Cubic Surfaces Via Periods of K3 Surfaces
• The Complex Ball-quotient Structure of the Moduli Space of Certain Sextic Curves
• Moduli of surfaces in ℙ³