FJRW theory is a formulation of physical Landau-Ginzburg models with a rich algebraic structure, rooted in enumerative geometry. As a consequence of a major physical conjecture, called the Landau-Ginzburg Calabi-Yau correspondence, several birational morphisms of Calabi-Yau orbifolds should correspond to isomorphisms in FJRW theory. In this paper it is shown that not only does this claim prove to be the case, but is a special case of a wider FJRW isomorphism theorem, which in turn allows for a proof of mirror symmetry for a new class of cases in the Landau-Ginzburg setting. We also obtain several interesting geometric applications regarding the Chen-Ruan cohomology of certain Calabi-Yau orbifolds.
Their result relies on the assumption that @math . In order to understand this restriction better, consider that there are two possible weight systems for @math yielding an elliptic curve and 44 possible weight systems for @math yielding a K3 surface with involution. Recall in this construction, we require our polynomials to be of the form . Only 48 of the 88 possible combinations of weight systems satisfy the gcd condition imposed in @cite_41 . In this article we generalize this result in two ways. We remove the restriction on gcd's, and we extend the construction to all dimensions.
@cite_41
1636544587
We prove that the Borcea-Voisin mirror pairs of Calabi-Yau three- folds admit projective birational models that satisfy the Berglund-Hubsch- Chiodo-Ruan transposition rule. This shows that the two mirror constructions provide the same mirror pairs, as soon as both can be defined.