2024/12/03 by Eleonore Faber, Faber, Eleonore, Bernd Schober +1 · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Mathematics and Applications #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.2412.02422
We study the connection between Conway-Coxeter frieze patterns and the data of the minimal resolution of a complex curve singularity: using Popescu-Pampu's notion of the lotus of a singularity, we describe a bijection between the dual resolution graphs of Newton non-degenerate plane curve singularities and Conway-Coxeter friezes. We use representation theoretic reduction methods to interpret some of the entries of the frieze coming from the partial resolutions of the corresponding curve singularity. Finally, we translate the notion of mutation, coming from cluster combinatorics, to resolutions of plane complex curves.