Frieze patterns and combinatorics of curve singularities
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912142389673984 |
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| author | Faber, Eleonore Schober, Bernd |
| author_facet | Faber, Eleonore Schober, Bernd |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_02422 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Frieze patterns and combinatorics of curve singularities Faber, Eleonore Schober, Bernd Algebraic Geometry Representation Theory 32S45 13F60 14H20 16G20 18G80 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. |
| title | Frieze patterns and combinatorics of curve singularities |
| topic | Algebraic Geometry Representation Theory 32S45 13F60 14H20 16G20 18G80 |
| url | https://arxiv.org/abs/2412.02422 |