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• W1796115931 abstract "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 the dual space defines another family ${cal F}(Delta^*)$ of Calabi-Yau varieties, so that we obtain the remarkable duality between two {em different families} of Calabi-Yau varieties. It is shown that the properties of this duality coincide with the properties of {em Mirror Symmetry} discovered by physicists for Calabi-Yau $3$-folds. Our method allows to construct many new examples of Calabi-Yau $3$-folds and new candidats for their mirrors which were previously unknown for physicists. We conjecture that there exists an isomorphism between two conformal field theories corresponding to Calabi-Yau varieties from two families ${cal F}(Delta)$ and ${cal F}(Delta^*)$." @default.
• W1796115931 created "2016-06-24" @default.
• W1796115931 creator A5058614926 @default.
• W1796115931 date "1993-10-01" @default.
• W1796115931 modified "2023-10-16" @default.
• W1796115931 title "Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties" @default.
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