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

Abstract

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.

6 pages, Latex file

Cited by in corpus (57)

• Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
• String Theory on Calabi-Yau Manifolds
• Global F-theory GUTs
• F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds
• Hypergeometric functions and mirror symmetry in toric varieties
• Small Cosmological Constants in String Theory
• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• A New Construction of Calabi-Yau Manifolds: Generalized CICYs
• On the Geometric Interpretation of N = 2 Superconformal Theories
• Supersymmetric partition functions on Riemann surfaces
• Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry
• Toric complete intersections and weighted projective space
• Compactification, Geometry and Duality: N=2
• Computational Tools for Cohomology of Toric Varieties
• PALP - a User Manual
• Lattice polarized toric K3 surfaces
• The Moduli Space of N = 2 Superconformal Field Theories
• Laurent Inversion
• A proposal for (0,2) mirrors of toric varieties
• Mirror Symmetry Constructions: A Review
• Box Graphs and Resolutions I
• The 14th case VHS via K3 fibrations
• Mirror Symmetry for Five-Parameter Hulek-Verrill Manifolds
• On the structure of supersymmetric T3 fibrations
• Mirror pairs of Calabi-Yau threefolds from mirror pairs of quasi-Fano threefolds
• Berglund-Hübsch mirror symmetry via vertex algebras
• Minuscule Schubert Varieties and Mirror Symmetry
• Degenerations and mirror contractions of Calabi-Yau complete intersections via Batyrev-Borisov Mirror symmetry
• The Breakdown of Topology at Small Scales
• Finding the Mirror of the Beauville Manifold
• Gromov-Witten Invariants via Algebraic Geometry
• Probing Geometry with Stability Conditions
• Strong McKay Correspondence, String-theoretic Hodge Numbers and Mirror Symmetry
• The making of Calabi-Yau spaces: Beyond toric hypersurfaces
• On the birationality of complete intersections associated to nef-partitions
• Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces
• Polytopes and Skeleta
• On Clifford double mirrors of toric complete intersections
• Special Lagrangian torus fibrations of complete intersection Calabi-Yau manifolds: a geometric conjecture
• Classical Weight-Four L-value Ratios as Sums of Calabi--Yau Invariants
• Mirror Symmetry and Partition Functions
• Versality in mirror symmetry
• Integral affine structures on spheres III: complete intersections
• A category of kernels for equivariant factorizations, II: further implications
• Lagrangian Torus Fibrations and Mirror Symmetry of Calabi-Yau Manifolds
• On stringy Euler characteristics of Clifford non-commutative varieties
• Gorenstein polytopes and their stringy E-functions
• Mixed toric residues and Calabi-Yau complete intersections
• Black Hole Condensation and the Web of Calabi-Yau Manifolds
• Complete intersection Calabi--Yau threefolds in Hibi toric varieties and their smoothing
• Generalized compactifications of Batyrev hypersurface families
• On smooth Gorenstein polytopes
• Toric Degenerations and Batyrev-Borisov Duality
• Orbifold Riemann-Roch for threefolds with an application to Calabi-Yau geometry
• Computing Cohomology on Toric Varieties
• A proof of the birationality of certain BHK-mirrors
• Mutation equivalence of toric Landau-Ginzburg models