Quantum ring of singularity $X^p+X{Y}^q$

Abstract

In this paper, we will prove that the quantum ring of the quasi-homogeneous polynomial $X^p+X{Y}^q(p\ge 2,q>1)$ with some admissible symmetry group $G$ defined by Fan-Jarvis-Ruan-Witten theory is isomorphic to the Milnor ring of its mirror dual polynomial $X^{p}Y+Y^q$. 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.

20 pages

References in corpus (1)

• A-twisted heterotic Landau-Ginzburg models

Cited by in corpus (1)

• FJRW-Rings and Landau-Ginzburg Mirror Symmetry in Two Dimensions