# Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

@article{Batyrev1993DualPA, title={Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties}, author={Victor V. Batyrev}, journal={Journal of Algebraic Geometry}, year={1993}, volume={3}, pages={493-545} }

We consider families ${\cal F}(\Delta)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $\Delta$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomials $f$ with a fixed $n$-dimensional Newton polyhedron $\Delta$ in $n$-dimensional algebraic torus ${\bf T} =({\bf C}^*)^n$. If the family ${\cal F}(\Delta)$ defined by a Newton polyhedron $\Delta$ consists of $(n-1)$-dimensional Calabi-Yau varieties, then the dual, or polar, polyhedron $\Delta^*$ in…

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