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

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.

arXiv commentLaTeX2e, 21 page, 6 figures

References in corpus (4)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• The Monomial-Divisor Mirror Map
• The Geometry Underlying Mirror Symmetry
• Mirror Symmetry via 3-tori for a class of Calabi-Yau Threefolds

Cited by in corpus (5)

• Topological mirror symmetry with fluxes
• Special Lagrangian Fibrations II: Geometry
• Lagrangian torus fibration of quintic Calabi-Yau hypersurfaces I: Fermat quintic case
• Moduli, Motives, Mirrors (Plenary talk at the 3rd ECM, Barcelona, July 10-14, 2000)
• Lagrangian Torus Fibrations and Mirror Symmetry of Calabi-Yau Manifolds