2010/08/19 by Sophie Morier-Genoud, Morier-Genoud, Sophie, Valentin Ovsienko +3 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO
paper · pdf · doi:10.48550/arxiv.1008.3359
36 pages, 4 figures, minor changes from the previous versions; references added (v2), section 5.5 added (v3), picture added (v4)
arxiv created 2011/07/18 · arxiv updated 2011/07/19
We study the space of 2-frieze patterns generalizing that of the classical Coxeter-Conway frieze patterns. The geometric realization of this space is the space of n-gons (in the projective plane and in 3-dimensional vector space) which is a close relative of the moduli space of genus 0 curves with n marked points. We show that the space of 2-frieze patterns is a cluster manifold and study its algebraic and arithmetic properties.