Torus Fibrations of Calabi-Yau Hypersurfaces in Toric Varieties and Mirror Symmetry
نویسنده
چکیده
We consider regular Calabi-Yau hypersurfaces in N -dimensional smooth toric varieties. On such a hypersurface in the neighborhood of the large complex structure limit point we construct a fibration over a sphere S whose generic fibers are tori T. Also for certain one-parameter families of such hypersurfaces we show that the monodromy transformation is induced by a translation of the T fibration by a section. Finally we construct a dual fibration and provide some evidence that it describes the mirror family.
منابع مشابه
S ep 1 99 9 Topological Mirror Symmetry
The Strominger-Yau-Zaslow conjecture proposes that mirror symmetry can be explained by the existence, in a mirror pair of Calabi-Yau manifolds, of dual special La-grangian T n-fibrations. (See [18,8,6,7] for further clarification of this conjecture.) Recently, Zharkov in [20] proved that non-singular Calabi-Yau hypersurfaces in toric varieties have topological T n-fibrations, and Ruan in [17] h...
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