# Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties

@article{Borisov1993TowardsTM, title={Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties}, author={Lev Borisov}, journal={arXiv: Algebraic Geometry}, year={1993} }

We propose a combinatorical duality for lattice polyhedra which conjecturally gives rise to the pairs of mirror symmetric families of Calabi-Yau complete intersections in toric Fano varieties with Gorenstein singularities. Our construction is a generalization of the polar duality proposed by Batyrev for the case of hypersurfaces.

## 120 Citations

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Generalizing the notions of reflexive polytopes and nef-partitions of Batyrev and Borisov, we propose a mirror symmetry construction for Calabi-Yau complete intersections in Fano toric varieties.

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Abstract. We prove in full generality the mirror duality conjecture for string-theoretic Hodge numbers of Calabi–Yau complete intersections in Gorenstein toric Fano varieties. The proof is based on…

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In this article, we summarize combinatorial description of complete intersection Calabi-Yau threefolds in Hibi toric varieties. Such Calabi-Yau threefolds have at worst conifold singularities, and…

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We describe Batyrev’s construction of the mirror to a family of Calabi–Yau hypersurfaces in a Fano toric variety, based on polar duality for lattice polytopes. We revisit the example of the quintic…

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