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Modular Curves and Mordell-Weil Torsion in F-theory
[article]
2019
arXiv
pre-print
In this work we prove a bound for the torsion in Mordell-Weil groups of smooth elliptically fibered Calabi-Yau 3- and 4-folds. In particular, we show that the set which can occur on a smooth elliptic Calabi-Yau n-fold for (n≥ 3) is contained in the set of subgroups which appear on a rational elliptic surface, and is slightly larger for n = 2. The key idea in our proof is showing that any elliptic fibration with sufficiently large torsion has singularities in codimension 2 which do not admit a
arXiv:1910.04095v2
fatcat:p3italufbveb7gp5l2sjfzmojq