Torus Fibrations of Calabi-Yau Hypersurfaces in Toric Varieties and Mirror Symmetry

1998/06/17 by Ilia Zharkov, Zharkov, Ilia
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.AG

paper · pdf · doi:10.48550/arxiv.math/9806091

LaTeX2e, 21 page, 6 figures

arxiv created 1998/06/17 · arxiv updated 2009/11/30

Abstract

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^N-1 whose generic fibers are tori T^N-1. Also for certain one-parameter families of such hypersurfaces we show that the monodromy transformation is induced by a translation of the T^N-1 fibration by a section. Finally we construct a dual fibration and provide some evidence that it describes the mirror family.

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