Extending the Picard-Fuchs system of local mirror symmetry

Abstract

We propose an extended set of differential operators for local mirror symmetry. If $X$ is Calabi-Yau such that $\dim H_4(X,\mathbb{Z})=0$, 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 $X=K_S$ through similar techniques. In addition, open string PF systems are considered.

47 pages, 7 figures. Minor errors corrected, including the correction of the triple intersection numbers for the del Pezzo surface

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