Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P 4 and Extensions of Landau-Ginzburg Theory (1995) [3 citations — 0 self]
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author = {Philip Candelas and Xenia de la Ossa and Sheldon Katz and Olden Lane},
title = {Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P 4 and Extensions of Landau-Ginzburg Theory},
year = {1995}
}
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Abstract:
Recently two groups have listed all sets of weights k = (k 1 ; : : : ; k 5 ) such that the weighted projective space IP 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 IP 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. * Supported in part by the Robert A. Welch Foundation, the Swiss National Science Foundation, a WorldLab...
Citations
| 159 | Introduction to toric varieties – Fulton - 1993 |
| 59 | The homogeneous coordinate ring of a toric variety – Cox - 1995 |
| 6 | Mirror symmetry for two parameter models – Candelas, Font, et al. - 1994 |
| 2 | Mirror Symmetry for Generic Hypersurfaces in Weighted Projective Spaces, in preparation – Berglund, Katz, et al. |
| 1 | private communication – Theisen |
| 1 | Mirror Symmetry Constructions: A review, IASSNSHEP -94/38 – Berglund, Katz |
| 1 | On the Hodge Structure – Batyrev, Cox |
