# Toric Geometry and Calabi-Yau Compactifications

@article{Kreuzer2006ToricGA, title={Toric Geometry and Calabi-Yau Compactifications}, author={Maximilian Kreuzer}, journal={arXiv: High Energy Physics - Theory}, year={2006} }

These notes contain a brief introduction to the construction of toric Calabi--Yau hypersurfaces and complete intersections with a focus on issues relevant for string duality calculations. The last two sections can be read independently and report on recent results and work in progress, including torsion in cohomology, classification issues and topological transitions.

## 44 Citations

Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists)

- Mathematics
- 2009

These lecture notes are an introduction to toric geometry. Particular focus is put on the description of toric local Calabi-Yau varieties, such as needed in applications to the AdS/CFT correspondence…

The making of Calabi‐Yau spaces: Beyond toric hypersurfaces

- Mathematics
- 2009

While Calabi‐Yau hypersurfaces in toric ambient spaces provide a huge number of examples, theoretical considerations as well as applications to string phenomenology often suggest a broader…

Computing Cohomology on Toric Varieties

- Mathematics
- 2011

In these notes a recently developed technique for the computation of line bundle-valued sheaf cohomology group dimensions on toric varieties is reviewed. The key result is a vanishing theorem for the…

Computational Tools for Cohomology of Toric Varieties

- MathematicsArXiv
- 2011

Applications to the computation of chiral massless matter spectra in string compactifications are discussed, and using the software package cohomCalg, its utility is highlighted on a new target space dual pair of (0,2) heterotic string models.

Towards Open String Mirror Symmetry for One-Parameter Calabi-Yau Hypersurfaces

- Mathematics
- 2008

This work is concerned with branes and differential equations for one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. For a certain class of B-branes we derive the inhomogeneous…

Toric construction of global F-theory GUTs

- Mathematics
- 2011

We systematically construct a large number of compact Calabi-Yau fourfolds which are suitable for F-theory model building. These elliptically fibered Calabi-Yaus are complete intersections of two…

Tops as building blocks for G2 manifolds

- Mathematics
- 2016

A bstractA large number of examples of compact G2 manifolds, relevant to supersymmetric compactifications of M-Theory to four dimensions, can be constructed by forming a twisted connected sum of two…

Cohomology of line bundles: Applications

- Mathematics
- 2012

Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for…

Toric K3-fibred Calabi-Yau manifolds with del Pezzo divisors for string compactifications

- Mathematics
- 2012

A bstractWe analyse several explicit toric examples of compact K3-fibred Calabi-Yau three-folds. These manifolds can be used for the study of string dualities and are crucial ingredients for the…

Combinatorics in N 1 Heterotic Vacua

- Mathematics
- 2011

We briefly review an algorithmic strategy to explore the landscape of heterotic 𝐸8×𝐸8 vacua, in the context of compactifying smooth Calabi-Yau threefolds with vector bundles. The Calabi-Yau…