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arXiv · 1809.05160

On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds

Yu-Chien Huang·Washington Taylor
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Abstract

We systematically analyze the fibration structure of toric hypersurface Calabi-Yau threefolds with large and small Hodge numbers. We show that there are only four such Calabi-Yau threefolds with $h^{1, 1} \geq 140$ or $h^{2, 1} \geq 140$ that do not have manifest elliptic or genus one fibers arising from a fibration of the associated 4D polytope. There is a genus one fibration whenever either Hodge number is 150 or greater, and an elliptic fibration when either Hodge number is 228 or greater. We find that for small $h^{1, 1}$ the fraction of polytopes in the KS database that do not have a genus one or elliptic fibration drops exponentially as $h^{1,1}$ increases. We also consider the different toric fiber types that arise in the polytopes of elliptic Calabi-Yau threefolds.

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Yu-Chien Huang, Washington Taylor. 2018-09-13. On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds. https://doi.org/10.1007/jhep03(2019)014

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