Gluing moduli spaces of quantum toric stacks via secondary fan

The extension from toric varieties to quantum toric stacks allows for the study of moduli spaces of toric objects with fixed combinatorial structures, as we now consider general finitely generated subgroups of $\mathbb{R}^n$ as "lattices." This paper aims to construct a moduli space that encompasses all such moduli spaces for a given dimension of the ambient space. To achieve this, we adapt the construction of the secondary fan within the quantum framework. This approach provides a description of wall-crossings between different moduli spaces, analogous to those observed in LVMB manifolds.