Hokkaido University Preprint Series in Mathematics
We propose an extended set of differential operators for local mirror symmetry. If X is Calabi-Yau such that dimH4(X,Z) = 0, then we show that our operators fully describe mirror symmetry. In the process, a conjecture for intersection theory for such X is uncovered. We also find new operators on several examples of type X = KS through similar techniques. In addition, open string PF systems are considered.