The Web of Calabi-Yau hypersurfaces in toric varieties

@article{Avram1997TheWO,
  title={The Web of Calabi-Yau hypersurfaces in toric varieties},
  author={A. Avram and M. Kreuzer and M. Mandelberg and H. Skarke},
  journal={Nuclear Physics},
  year={1997},
  volume={505},
  pages={625-640}
}
Abstract Recent results on duality between string theories and connectedness of their moduli spaces seem to go a long way toward establishing the uniqueness of an underlying theory. For the large class of Calabi-Yau 3-folds that can be embedded as hypersurfaces in toric varieties the proof of mathematical connectedness via singular limits is greatly simplified by using polytopes that are maximal with respect to certain single or multiple weight systems. We identify the multiple weight systems… Expand

Figures and Tables from this paper

Heterotic bundles on Calabi-Yau manifolds with small Picard number
A bstractWe undertake a systematic scan of vector bundles over spaces from the largest database of known Calabi-Yau three-folds, in the context of heterotic string compactification. Specifically, weExpand
Families of Calabi–Yau hypersurfaces in Q-Fano toric varieties
Abstract We provide a sufficient condition for a general hypersurface in a Q -Fano toric variety to be a Calabi–Yau variety in terms of its Newton polytope. Moreover, we define a generalization ofExpand
Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians
Abstract In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of rationalExpand
Extremal Bundles on Calabi–Yau Threefolds
We study constructions of stable holomorphic vector bundles on Calabi–Yau threefolds, especially those with exact anomaly cancellation which we call extremal. By going through the known databases weExpand
Complete classification of reflexive polyhedra in four dimensions
Four dimensional reflexive polyhedra encode the data for smooth Calabi-Yau threefolds that are hypersurfaces in toric varieties, and have important applications both in perturbative and inExpand
Calabi-Yau 4-folds and toric fibrations
Abstract We present a general scheme for identifying fibrations in the framework of toric geometry and provide a large list of weights for Calabi-Yau 4-folds. We find 914 164 weights with degree d ≤Expand
NC Calabi–Yau orbifolds in toric varieties with discrete torsion
Using the algebraic geometric approach of Berenstein et al (hep-th/005087 and hep-th/009209) and methods of toric geometry, we study non-commutative (NC) orbifolds of Calabi-Yau hypersurfaces inExpand
Universal Calabi-Yau algebra: Towards an unification of complex geometry
We present a universal normal algebra suitable for constructing and classifying Calabi–Yau spaces in arbitrary dimensions. This algebraic approach includes natural extensions of reflexive weightExpand
Divisors on elliptic Calabi-Yau 4-folds and the superpotential in F-theory, I
Each smooth elliptic Calabi-Yau 4-fold determines both a three-dimensional physical theory (a compactification of ``M-theory'') and a four-dimensional physical theory (using the ``F-theory''Expand
Calabi-Yau Spaces in the String Landscape
Calabi-Yau spaces, or Kahler spaces admitting zero Ricci curvature, have played a pivotal role in theoretical physics and pure mathematics for the last half-century. In physics, they constituted theExpand
...
1
2
3
4
...

References

SHOWING 1-10 OF 62 REFERENCES
Rolling Among Calabi-Yau Vacua
Abstract For a very large number of Calabi-Yau manifolds of many different numerical invariants and hence distinct homotopy types, the relevant moduli spaces can be assembled into a connected web.Expand
Calabi-Yau manifolds as complete intersections in products of complex projective spaces
We consider constructions of manifolds withSU(3) holonomy as embedded in products of complex projective spaces by imposing certain homogeneous holomorphic constraints. We prove that every suchExpand
Calabi-Yau manifolds in weighted P4
Abstract It has recently been recognized that the relation between exactly solvable conformal field theory compactifications of the Heterotic String and Calabi-Yau manifolds necessarily involves theExpand
On the connectedness of the moduli space of Calabi-Yau manifolds
We show that the moduli space of all Calabi-Yau manifolds that can be realized as hypersurfaces described by a transverse polynomial in a four-dimensional weighted projective space, is connected.Expand
Compactifications of F-theory on Calabi-Yau threefolds. (I)
Abstract We continue our study of compactifications of F-theory on Calabi-Yau threefolds. We gain more insight into F-theory duals of heterotic strings and provide a recipe for building F-theoryExpand
The monomial-divisor mirror map
For each family of Calabi-Yau hypersurfaces in toric varieties, Batyrev has proposed a possible mirror partner (which is also a family of Calabi-Yau hypersurfaces). We explain a natural constructionExpand
UNIFICATION OF M- AND F-THEORY CALABI-YAU FOURFOLD VACUA
Abstract We consider splitting-type phase transitions between Calabi-Yau fourfolds. These transitions generalize previously known types of conifold transitions between threefolds. Similar to conifoldExpand
Searching for K3 fibrations
Abstract We present two methods for studying fibrations of Calabi-Yau manifolds embedded in toric varieties described by single weight systems. We analyze 184 026 such spaces and identify among themExpand
Complete intersection Calabi-Yau manifolds
An investigation is made of a class of Calabi-Yau spaces for which the manifold may be represented as a complete intersection of polynomials in a product of projective spaces. There are at least aExpand
Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties
Abstract The moduli dependence of (2,2) superstring compactifications based on Calabi-Yau hypersurfaces in weighted projective space has so far only been investigated for Fermat-type polynomialExpand
...
1
2
3
4
5
...