Abstract
Let W∈C[x1,⋯,xN] be an invertible polynomial with an isolated singularity at origin, and let G⊂SLN∩(C⁎)N be a finite diagonal and special linear symmetry group of W. In this paper, we use the category MFG(W) of G-equivariant matrix factorizations and its associated VSHS to construct a G-equivariant version of Saito's theory of primitive forms. We prove there exists a canonical categorical primitive form of MFG(W) characterized by GWmax-equivariance. Conjecturally, this G-equivariant Saito theory is equivalent to the genus zero part of the FJRW theory under LG/LG mirror symmetry. In the marginal deformation direction, we verify this for the FJRW theory of (15(x15+⋯+x55),Z/5Z) with its mirror dual B-model Landau-Ginzburg orbifold (15(x15+⋯+x55),(Z/5Z)4). In the case of the Quintic family W=15(x15+⋯+x55)−ψx1x2x3x4x5, we also prove a comparison result of B-model VSHS's conjectured by Ganatra-Perutz-Sheridan [14].
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
