Cohomology of line bundles: Applications

@article{Blumenhagen2012CohomologyOL,
  title={Cohomology of line bundles: Applications},
  author={Ralph Blumenhagen and Benjamin Jurke and Thorsten Rahn and Helmut Roschy},
  journal={Journal of Mathematical Physics},
  year={2012},
  volume={53},
  pages={012302}
}
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 the computation of line bundle valued cohomology classes over toric varieties are presented. For the heterotic string, the prime examples are so-called monad constructions on Calabi-Yau manifolds. In the context of Type II orientifolds, one often needs to compute cohomology for line bundles on… 

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References

SHOWING 1-10 OF 36 REFERENCES
Vector bundle extensions, sheaf cohomology, and the heterotic standard model
Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we
Monad bundles in heterotic string compactifications
In this paper, we study positive monad vector bundles on complete intersection Calabi-Yau manifolds in the context of E8 × E8 heterotic string compactifications. We show that the class of such
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
Heterotic Compactification, An Algorithmic Approach
We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in
Cohomology of Line Bundles
In this chapter we compute the dimension of every cohomology group of every line bundle L on a complex torus X = V/∧ (see Theorem 3.5.5). As a direct consequence we get a formula for the
Closed form expressions for Hodge numbers of complete intersection Calabi-Yau threefolds in toric varieties
We use Batyrev-Borisov's formula for the generating function of stringy Hodge numbers of Calabi-Yau varieties realized as complete intersections in toric varieties in order to get closed form
Cohomology of toric line bundles via simplicial Alexander duality
We give a rigorous mathematical proof for the validity of the toric sheaf cohomology algorithm conjectured in the recent paper by Blumenhagen, Jurke, Rahn, and Roschy (arXiv:1003.5217). We actually
Introduction to Toric Varieties.
Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic
Target space duality for (0,2) compactifications
(0,2) elephants
A bstractWe enumerate massless E6 singlets for (0,2)-compactifications of the heterotic string on a Calabi-Yau threefold with the “standard embedding” in three distinct ways. In the large radius
...
...