Cluster scattering diagrams via quiver moduli and tight gradings
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914163238895616 |
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| author | Burcroff, Amanda Lee, Kyungyong Mou, Lang Musiker, Gregg Reineke, Markus |
| author_facet | Burcroff, Amanda Lee, Kyungyong Mou, Lang Musiker, Gregg Reineke, Markus |
| contents | We study rank-2 cluster scattering diagrams through moduli spaces of quiver representations and a recently developed combinatorial framework of tight gradings. Combining quiver-theoretic and combinatorial methods, we prove and extend a collection of conjectures posed by Elgin--Reading--Stella concerning the structural and enumerative properties of the wall-function coefficients. The tight grading perspective also provides a new proof of the Weyl group symmetry of the scattering diagram. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cluster scattering diagrams via quiver moduli and tight gradings Burcroff, Amanda Lee, Kyungyong Mou, Lang Musiker, Gregg Reineke, Markus Combinatorics Algebraic Geometry Representation Theory 13F60, 05E10, 05A15 We study rank-2 cluster scattering diagrams through moduli spaces of quiver representations and a recently developed combinatorial framework of tight gradings. Combining quiver-theoretic and combinatorial methods, we prove and extend a collection of conjectures posed by Elgin--Reading--Stella concerning the structural and enumerative properties of the wall-function coefficients. The tight grading perspective also provides a new proof of the Weyl group symmetry of the scattering diagram. |
| title | Cluster scattering diagrams via quiver moduli and tight gradings |
| topic | Combinatorics Algebraic Geometry Representation Theory 13F60, 05E10, 05A15 |
| url | https://arxiv.org/abs/2511.14672 |