Quantum ring of singularity Xᵖ+XYq

الأصل · EN

In this paper, we will prove that the quantum ring of the quasi-homogeneous polynomial Xᵖ+XYq(p≥ 2,q>1) with some admissible symmetry group G defined by Fan-Jarvis-Ruan-Witten theory is isomorphic to the Milnor ring of its mirror dual polynomial XᵖY+Yq. We will construct an concrete isomorphism between them. The construction is a little bit different in case (p-1,q)=1 and case (p-1,q)=d>1. Some other problems including the correspondence between the pairings of both Frobenius algebras has also been discussed.