• Corpus ID: 18222916

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

  title={Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties},
  author={Victor V. Batyrev},
  journal={Journal of Algebraic Geometry},
  • V. Batyrev
  • Published 1 October 1993
  • Mathematics
  • Journal of Algebraic Geometry
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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