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

Berenstein and Zelevinsky introduced quantum cluster algebras BZ1 and the triangular bases BZ2. The support conjecture proposed in LLRZ, 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 L 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.