Prepotentials for local mirror symmetry via Calabi-Yau fourfolds
Abstract
In this paper, we first derive an intrinsic definition of classical triple intersection numbers of KS, where S is a complex toric surface, and use this to compute the extended Picard-Fuchs system of KS of our previous paper, without making use of the instanton expansion. We then extend this formalism to local fourfolds KX, where X is a complex 3-fold. As a result, we are able to fix the prepotential of local Calabi-Yau threefolds KS up to polynomial terms of degree 2. We then outline methods of extending the procedure to non canonical bundle cases.
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