# 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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