Formulae for Line Bundle Cohomology on Calabi‐Yau Threefolds

@article{Constantin2019FormulaeFL,
  title={Formulae for Line Bundle Cohomology on Calabi‐Yau Threefolds},
  author={Andrei Constantin and Andr{\'e} Lukas},
  journal={Fortschritte der Physik},
  year={2019},
  volume={67}
}
We present closed form expressions for the ranks of all cohomology groups of holomorphic line bundles on several Calabi‐Yau threefolds realised as complete intersections in products of projective spaces. The formulae have been obtained by systematising and extrapolating concrete calculations and they have been checked computationally. Although the intermediate calculations often involve laborious computations of ranks of Leray maps in the Koszul spectral sequence, the final results for… 

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References

SHOWING 1-10 OF 46 REFERENCES

Line Bundle Cohomologies on CICYs with Picard Number Two

We analyse line bundle cohomologies on all favourable co‐dimension two Complete Intersection Calabi Yau (CICY) manifolds of Picard number two. Our results provide further evidence that the cohomology

The moduli space of heterotic line bundle models: a case study for the tetra-quadric

A bstractIt has recently been realised that polystable, holomorphic sums of line bundles over smooth Calabi-Yau three-folds provide a fertile ground for heterotic model building. Large numbers of

Immaculate line bundles on toric varieties

We call a sheaf on an algebraic variety immaculate if it lacks any cohomology including the zero-th one, that is, if the derived version of the global section functor vanishes. Such sheaves are the

New Calabi‐Yau manifolds with small Hodge numbers

It is known that many Calabi‐Yau manifolds form a connected web. The question of whether all Calabi‐Yau manifolds form a single web depends on the degree of singularity that is permitted for the

Calabi‐Yau Manifolds: A Bestiary for Physicists

Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or equivalently, with trivial canonical bundle (canonical class). They are used to construct possibly realistic (super)string

Hodge numbers for CICYs with symmetries of order divisible by 4

We compute the Hodge numbers for the quotients of complete intersection Calabi‐Yau three‐folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of

Heterotic line bundle models on elliptically fibered Calabi-Yau three-folds

A bstractWe analyze heterotic line bundle models on elliptically fibered Calabi-Yau three-folds over weak Fano bases. In order to facilitate Wilson line breaking to the standard model group, we focus

Calabi‐Yau Threefolds with Small Hodge Numbers

We present a list of Calabi‐Yau threefolds known to us, and with holonomy groups that are precisely SU(3) , rather than a subgroup, with small Hodge numbers, which we understand to be those manifolds

Hodge numbers for all CICY quotients

A bstractWe present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies

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