Mirror symmetry and elliptic Calabi-Yau manifolds

Abstract

We find that for many Calabi-Yau threefolds with elliptic or genus one fibrations mirror symmetry factorizes between the fiber and the base of the fibration. In the simplest examples, the generic CY elliptic fibration over any toric base surface $B$ that supports an elliptic Calabi-Yau threefold has a mirror that is an elliptic fibration over a dual toric base surface $\tilde{B}$ that is related through toric geometry to the line bundle $-6K_B$. The Kreuzer-Skarke database includes all these examples and gives a wide range of other more complicated constructions where mirror symmetry also factorizes. Since recent evidence suggests that most Calabi-Yau threefolds are elliptic or genus one fibered, this points to a new way of understanding mirror symmetry that may apply to a large fraction of smooth Calabi-Yau threefolds. The factorization structure identified here can also apply for Calabi-Yau manifolds of higher dimension.

arXiv comment30 pages, 6 figures; v2: corrected Table 1, added references

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Cited by in corpus (5)

• F-Theory on Quotients of Elliptic Calabi-Yau Threefolds
• Fibration structure in toric hypersurface Calabi-Yau threefolds
• On the Elliptic Calabi-Yau Fourfold with Maximal $h^{1,1}$
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• A Database of Calabi-Yau Orientifolds and the Size of D3-Tadpoles