• Corpus ID: 221470285

Cohomology Chambers on Complex Surfaces and Elliptically Fibered Calabi-Yau Three-folds

@article{Brodie2020CohomologyCO,
  title={Cohomology Chambers on Complex Surfaces and Elliptically Fibered Calabi-Yau Three-folds},
  author={Callum R. Brodie and Andrei Constantin},
  journal={arXiv: High Energy Physics - Theory},
  year={2020}
}
We determine several classes of smooth complex projective surfaces on which Zariski decomposition can be combined with vanishing theorems to yield cohomology formulae for all line bundles. The obtained formulae express cohomologies in terms of divisor class intersections, and are adapted to the decomposition of the effective cone into Zariski chambers. In particular, we show this occurs on generalised del Pezzo surfaces, toric surfaces, and K3 surfaces. In the second part we use these surface… 

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References

SHOWING 1-10 OF 56 REFERENCES

Index Formulae for Line Bundle Cohomology on Complex Surfaces

We conjecture and prove closed‐form index expressions for the cohomology dimensions of line bundles on del Pezzo and Hirzebruch surfaces. Further, for all compact toric surfaces we provide a simple

Topological Formulae for the Zeroth Cohomology of Line Bundles on Surfaces

We identify a set of transforms on the Picard lattice of non-singular complex projective surfaces that map effective line bundles to nef line bundles, while preserving the dimension of the zeroth

Formulae for Line Bundle Cohomology on Calabi‐Yau Threefolds

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

When are Zariski chambers numerically determined?

Abstract The big cone of every smooth projective surface X admits a natural decomposition into Zariski chambers. The purpose of this note is to give a simple criterion for the interiors of all

Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts

We study elliptically fibered K3 surfaces, with sections, in toric Fano threefolds which satisfy certain combinatorial properties relevant to F-theory/Heterotic duality. We show that some of these

Weyl and Zariski chambers on K3 surfaces

Abstract. The big cone of every K3 surface admits two natural chamber decompositions: the decomposition into Zariski chambers, and the decomposition into simple Weyl chambers. In the present paper we

Singular del Pezzo surfaces whose universal torsors are hypersurfaces

We classify all generalized del Pezzo surfaces (that is, minimal desingularizations of singular del Pezzo surfaces containing only rational double points) whose universal torsors are open subsets of

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

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
...