Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-12-13
Nucl.Phys. B450 (1995) 267-292
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, plain TeX. Two figures submitted separately as a uuencoded file. A plot at the end of the paper requires an extended
Scientific paper
10.1016/0550-3213(95)00189-Y
Recently two groups have listed all sets of weights (k_1,...,k_5) such that the weighted projective space P_4^{(k_1,...,k_5)} admits a transverse Calabi-Yau hypersurface. It was noticed that the corresponding Calabi-Yau manifolds do not form a mirror symmetric set since some 850 of the 7555 manifolds have Hodge numbers (b_{11},b_{21}) whose mirrors do not occur in the list. By means of Batyrev's construction we have checked that each of the 7555 manifolds does indeed have a mirror. The `missing mirrors' are constructed as hypersurfaces in toric varieties. We show that many of these manifolds may be interpreted as non-transverse hypersurfaces in weighted P_4's, ie, hypersurfaces for which dp vanishes at a point other than the origin. This falls outside the usual range of Landau--Ginzburg theory. Nevertheless Batyrev's procedure provides a way of making sense of these theories.
Candelas Philip
Katz Sheldon
la Ossa Xenia de
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