IASM Preprint Series 2020-01:Quantum K-theory of toric varieties, level structures, and 3D mirror symmetry


Abstract. We introduce a new version of 3d mirror symmetry for toric stacks, inspired by a 3d N = 2 abelian mirror symmetry construction in physics. Given some toric data, we introduce the K-theoretic I-function with effective level structure for the associated toric stack. When a particular stability condition is chosen, it restricts to the I-function for the particular toric GIT quotient. The mirror of a toric stack is defined by the Gale dual of the original toric data. We then proved the mirror conjecture that the I-functions of a mirror pair coincide, under the mirror map, which switches K¨ahler and equivariant parameters, and maps q !→ q−1.