Hodge theoretic mirror symmetry for toric stacks
Using the mirror theorem [CCIT15] we give a Landau Ginzburg mirror description for the big equivariant quantum cohomology of toric Deligne Mumford stacks. More precisely, we prove that the big equivariant quantum D module of a toric Deligne Mumford stack is isomorphic to the Saito structure associated to the mirror Landau Ginzburg potential. We give a GKZ style presentation of the quantum D module, and a combinatorial description of quantum cohomology as a quantum Stanley Reisner ring. We establish the convergence of the mirror isomorphism and of quantum cohomology in the big and equivariant setting.