# 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

#### 36 Citations

Heterotic bundles on Calabi-Yau manifolds with small Picard number

- Physics
- 2011

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, we… Expand

Families of Calabi–Yau hypersurfaces in Q-Fano toric varieties

- Mathematics
- 2016

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 of… Expand

Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians

- Physics, Mathematics
- 1998

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 rational… Expand

Extremal Bundles on Calabi–Yau Threefolds

- Mathematics, Physics
- 2015

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 we… Expand

Complete classification of reflexive polyhedra in four dimensions

- Physics, Mathematics
- 2000

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 in… Expand

Calabi-Yau 4-folds and toric fibrations

- Mathematics, Physics
- 1998

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

- Physics, Mathematics
- 2002

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 in… Expand

Universal Calabi-Yau algebra: Towards an unification of complex geometry

- Physics
- 2002

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 weight… Expand

Divisors on elliptic Calabi-Yau 4-folds and the superpotential in F-theory, I

- Mathematics, Physics
- 1997

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

- Physics, Mathematics
- 2020

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 the… Expand

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