2-frieze patterns and the cluster structure of the space of polygons
Copyright policy )2-frieze patterns and the cluster structure of the space of polygons
We study 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.
- UNIVERSITE JEAN MONNET SAINT-ETIENNE France
- Sorbonne Université France
- Université Paris Cité France
- Institut de Mathématiques de Jussieu France
- Pennsylvania State University United States
Cluster algebras, pentagram map, Real and complex geometry, 510, Mathematics - Algebraic Geometry, Projective techniques in algebraic geometry, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Coxeter-Conway friezes, FOS: Mathematics, moduli space, Mathematics - Combinatorics, frieze patterns, Combinatorics (math.CO), [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], Algebraic Geometry (math.AG), cluster algebra
Cluster algebras, pentagram map, Real and complex geometry, 510, Mathematics - Algebraic Geometry, Projective techniques in algebraic geometry, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Coxeter-Conway friezes, FOS: Mathematics, moduli space, Mathematics - Combinatorics, frieze patterns, Combinatorics (math.CO), [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], Algebraic Geometry (math.AG), cluster algebra
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