• Corpus ID: 117113433

Toric Geometry and Calabi-Yau Compactifications

  title={Toric Geometry and Calabi-Yau Compactifications},
  author={Maximilian Kreuzer},
  journal={arXiv: High Energy Physics - Theory},
  • M. Kreuzer
  • Published 29 December 2006
  • Mathematics
  • arXiv: High Energy Physics - Theory
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. 
Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists)
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
2 Toric Construction of Calabi-Yau three-folds
We briefly review an algorithmic strategy to explore the landscape of heterotic E8×E8 vacua, in the context of compactifying smooth Calabi-Yau three-folds with vector bundles. The Calabi-Yau
The making of Calabi‐Yau spaces: Beyond toric hypersurfaces
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
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
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
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
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
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
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
Cohomology of line bundles: A computational algorithm
We present an algorithm for computing line bundle valued cohomology classes over toric varieties. This is the basic starting point for computing massless modes in both heterotic and type IIB/F-theory