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On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds
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On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds
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On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds
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Journal Article
On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds
2019
Overview
A
bstract
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
≥ 140 or
h
2,1
≥ 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.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V,Springer Berlin,SpringerOpen
