### Abstract

Recently two groups have listed all sets of weights k = (k_{l},..., k_{5}) such that the weighted projective space P_{4}^{k} 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, i.e. 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.

Original language | English (US) |
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Pages (from-to) | 267-290 |

Number of pages | 24 |

Journal | Nuclear Physics, Section B |

Volume | 450 |

Issue number | 1-2 |

DOIs | |

State | Published - Sep 11 1995 |

Externally published | Yes |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

_{4}and extensions of Landau-Ginzburg theory.

*Nuclear Physics, Section B*,

*450*(1-2), 267-290. https://doi.org/10.1016/0550-3213(95)00189-Y