Denseness of $g$-vector cones from weighted orbifolds

Abstract

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 ${\mathbb{R}}^n$.

arXiv comment21 pages. this article draws heavily from arXiv:1904.12479, v2: minor corrections

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