2-frieze patterns and the cluster structure of the space of polygons

Details 2-frieze patterns and the cluster structure of the space of polygons 2-frieze patterns and the cluster structure of the space of polygons

2010-08-19

arxiv.org/abs/1008.3359v5

Mathematics

Algebraic Geometry

36 pages, 4 figures, minor changes from the previous versions; references added (v2), section 5.5 added (v3), picture added (v

Scientific paper

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.

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