Using the mirror theorem , 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 Gelfand–Kapranov–Zelevinsky (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.
"Hodge-theoretic mirror symmetry for toric stacks." J. Differential Geom. 114 (1) 41 - 115, January 2020. https://doi.org/10.4310/jdg/1577502022