• Corpus ID: 17913677

# 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}
}
• L. Borisov
• Published 2 October 1993
• Mathematics
• arXiv: Algebraic Geometry
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
Mirror Symmetry for Calabi-Yau complete intersections in Fano toric varieties
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.
Toric residue mirror conjecture for Calabi-Yau complete intersections
We generalize the toric residue mirror conjecture of Batyrev and Materov to not necessarily reflexive polytopes. Using this generalization we prove the toric residue mirror conjecture for Calabi-Yau
Degenerations and mirror contractions of Calabi-Yau complete intersections via Batyrev-Borisov Mirror symmetry
We show that the dual of the Cayley cone, associated to a Minkowski sum decomposition of a reflexive polytope, contains a reflexive polytope admitting a nef-partition. This nef-partition corresponds
Hypergeometric functions and mirror symmetry in toric varieties
We study aspects related to Kontsevich's homological mirror symmetry conjecture in the case of Calabi-Yau complete intersections in toric varieties. In a 1996 lecture at Rutgers University,
Mirror duality and string-theoretic Hodge numbers
• Mathematics
• 1995
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
Complete intersection Calabi–Yau threefolds in Hibi toric varieties and their smoothing
• Makoto Miura
• Mathematics
Algebraic and Geometric Combinatorics on Lattice Polytopes
• 2019
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
Batyrev Mirror Symmetry
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

## References

SHOWING 1-2 OF 2 REFERENCES
Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties
• Mathematics
• 1993
We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV1,...,Vr in a toric
Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
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