Denseness of $g$-vector cones from weighted orbifolds
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914222210809856 |
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| author | Yurikusa, Toshiya |
| author_facet | Yurikusa, Toshiya |
| contents | We study $g$-vector cones in a cluster algebra defined from a weighted orbifold of rank $n$ introduced by Felikson, Shapiro and Tumarkin. We determine the closure of the union of the $g$-vector cones. It is equal to $\mathbb{R}^n$ except for a weighted orbifold with empty boundary and exactly one puncture, in which case it is equal to the half space of a certain explicit hyperplane in $\mathbb{R}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02282 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Denseness of $g$-vector cones from weighted orbifolds Yurikusa, Toshiya Combinatorics Geometric Topology Rings and Algebras Representation Theory 13F60, 16G20 We study $g$-vector cones in a cluster algebra defined from a weighted orbifold of rank $n$ introduced by Felikson, Shapiro and Tumarkin. We determine the closure of the union of the $g$-vector cones. It is equal to $\mathbb{R}^n$ except for a weighted orbifold with empty boundary and exactly one puncture, in which case it is equal to the half space of a certain explicit hyperplane in $\mathbb{R}^n$. |
| title | Denseness of $g$-vector cones from weighted orbifolds |
| topic | Combinatorics Geometric Topology Rings and Algebras Representation Theory 13F60, 16G20 |
| url | https://arxiv.org/abs/2307.02282 |