Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and Extensions of Landau Ginzburg Theory
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 manifold...
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| Format: | Journal article |
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1994
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| _version_ | 1797066294383607808 |
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| author | Candelas, P Ossa, X Katz, S |
| author_facet | Candelas, P Ossa, X Katz, S |
| author_sort | Candelas, P |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T21:40:25Z |
| format | Journal article |
| id | oxford-uuid:47bdeaaa-0a6f-4f73-ba2d-0d91de421388 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:40:25Z |
| publishDate | 1994 |
| record_format | dspace |
| spelling | oxford-uuid:47bdeaaa-0a6f-4f73-ba2d-0d91de4213882022-03-26T15:21:42ZMirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and Extensions of Landau Ginzburg TheoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:47bdeaaa-0a6f-4f73-ba2d-0d91de421388Symplectic Elements at Oxford1994Candelas, POssa, XKatz, SRecently 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. |
| spellingShingle | Candelas, P Ossa, X Katz, S Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and Extensions of Landau Ginzburg Theory |
| title | Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and
Extensions of Landau Ginzburg Theory |
| title_full | Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and
Extensions of Landau Ginzburg Theory |
| title_fullStr | Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and
Extensions of Landau Ginzburg Theory |
| title_full_unstemmed | Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and
Extensions of Landau Ginzburg Theory |
| title_short | Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and
Extensions of Landau Ginzburg Theory |
| title_sort | mirror symmetry for calabi yau hypersurfaces in weighted p 4 and extensions of landau ginzburg theory |
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