Abstract:
All possible Calabi-Yau manifolds realisable as complete intersections and quotients of complete intersections by projectively-inherited symmetries are considered. We develop a stringent set of criteria with which to exhaustively search this huge class for three-generation manifolds. We find only one manifold meeting our conditions - namely the first manifold discovered by Yau. In addition it is shown that all known three-generation Calabi-Yau manifolds are either diffeomorphic to this one example or ill-defined. © 1987.
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