Nakajima’s quiver varieties and triangular bases of bipartite cluster algebras

Berenstein and Zelevinsky introduced quantum cluster algebras [Adv. Math. 195 (2005), no. 2, 405–455] and the triangular bases [Int. Math. Res. Not. 6 (2014), 1651–1688]. The support conjecture proposed in [Proc. Natl. Acad. Sci. USA 111 (2014), no. 27, 9712–9716], which asserts that the support of each triangular basis element for a rank-2 cluster algebra is bounded by an explicitly described region, was established in [J. Algebra 634 (2023), 97–164] for skew-symmetric rank-2 cluster algebras. In this paper we extend this result by proving a bound on the support of each triangular basis element for bipartite cluster algebras.