Scattering fans
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2017
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| _version_ | 1866910212403757056 |
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| author | Reading, Nathan |
| author_facet | Reading, Nathan |
| contents | Scattering diagrams arose in the context of mirror symmetry, Donaldson-Thomas theory, and integrable systems. We show that a consistent scattering diagram with minimal support cuts the ambient space into a complete fan. A special class of scattering diagrams, the cluster scattering diagrams, are closely related to cluster algebras. We show that the cluster scattering fan associated to an exchange matrix $B$ refines the mutation fan for $B$ (a complete fan that encodes the geometry of mutations of $B$). We conjecture that, when $B$ is $n\times n$ for $n>2$, these two fans coincide if and only if $B$ is of finite mutation type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_06968 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Scattering fans Reading, Nathan Combinatorics Algebraic Geometry Representation Theory 13F60, 14N35, 52C99 Scattering diagrams arose in the context of mirror symmetry, Donaldson-Thomas theory, and integrable systems. We show that a consistent scattering diagram with minimal support cuts the ambient space into a complete fan. A special class of scattering diagrams, the cluster scattering diagrams, are closely related to cluster algebras. We show that the cluster scattering fan associated to an exchange matrix $B$ refines the mutation fan for $B$ (a complete fan that encodes the geometry of mutations of $B$). We conjecture that, when $B$ is $n\times n$ for $n>2$, these two fans coincide if and only if $B$ is of finite mutation type. |
| title | Scattering fans |
| topic | Combinatorics Algebraic Geometry Representation Theory 13F60, 14N35, 52C99 |
| url | https://arxiv.org/abs/1712.06968 |