Work

Frieze patterns and combinatorics of curve singularities

Year: 2024

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2412.02422

Authors: Faber, Eleonore, Schober, Bernd

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation, Mathematisches Forschungsinstitut Oberwolfach, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences

Awards: G1009929464, Mathematical Sciences Research Institute (MSRI), G329468232, G4972001970, G6019427330, G7692653605, Research - Mathematical Sciences Research Institute (2021)

OpenAlex ID: W4405035777

Cites:

Cited by:

Related to: 10