| Homological mirror symmetry introduced by Kontsevich [Kon95a] greatly enriches the numerical approach to mirror symmetry investigated by Batyrev-Borisov [BB94], Givental [Giv98b], and many others. In this dissertation we introduce a duality construction which generalizes all existing mirror constructions. This construction is based on an object from physics called a Landau-Ginzburg model. It is our hope that this construction will be useful in finding mirrors in the sense of homological mirror symmetry. We provide several examples which illustrate the potential of this new approach. |
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