Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions
arXiv:0802.3376
Abstract
We construct a surprisingly large class of new Calabi-Yau 3-folds with small Picard numbers and propose a construction of their mirrors using smoothings of toric hypersurfaces with conifold singularities. These new examples are related to the previously known ones via conifold transitions. Our results generalize the mirror construction for Calabi-Yau complete intersections in Grassmannians and flag manifolds via toric degenerations. There exist exactly 198849 reflexive 4-polytopes whose 2-faces are only triangles or parallelograms of minimal volume. Every such polytope gives rise to a family of Calabi-Yau hypersurfaces with at worst conifold singularities. Using a criterion of Namikawa we found 30241 reflexive 4-polytopes such that the corresponding Calabi-Yau hypersurfaces are smoothable by a flat deformation. In particular, we found 210 reflexive 4-polytopes defining 68 topologically different Calabi--Yau 3-folds with . We explain the mirror construction and compute several new Picard--Fuchs operators for the respective 1-parameter families of mirror Calabi-Yau 3-folds.
arXiv commentminor corrections
References in corpus (10)
- Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
- PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
- Quantum Cohomology Rings of Toric Manifolds
- Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
- Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
- Complete classification of reflexive polyhedra in four dimensions
- Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds
- Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry
- Worldsheet Instantons, Torsion Curves, and Non-Perturbative Superpotentials
- Toric complete intersections and weighted projective space