Variation of GIT and variation of Lagrangian skeletons II: Quasi-symmetric case

Consider (C?)k acting on CN satisfying certain ‘quasi-symmetric’ condition which produces a class of toric Calabi-Yau GIT quotient stacks. Using subcategories Coh([CN/(C?)k]) generated by line bundles whose weights are inside zonotope called the ‘magic window’, Halpern-Leistner and Sam give combinatorial construction equivalences between derived categories coherent sheaves for various quotients. We apply coherent-constructible correspondence varieties to magic windows obtain non-characteristic deformation Lagrangian skeletons in T?RN?k parameterized Rk, exhibiting A-models phases. Moreover, translating window we universal skeleton over Rk×Rk?D some fattening D periodic facet hyperplane arrangement zonotope, show that induces local system Rk×Rk?D. also connect our results perverse schober structure identified Špenko Van den Bergh.