CALABI-YAU MANIFOLDS IN WEIGHTED P4

It has recently been recognized that the relation between exactly solvable conformal field theory compactifications of the Heterotic String and Calabi-Yau manifolds necessarily involves the discussion of embeddings in weighted projective space. We therefore study this class of manifolds more closely. We have constructed a subclass of these spaces and find that this class features a surprising symmetry under χ → -χ. Furthermore, we show that this class is potentially of much greater interest with regard to phenomenologically viable models, as there are 25 three-generation models among these manifolds. © 1990.