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Modular curves and Mordell-Weil torsion in F-theory

2020
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Journal of High Energy Physics
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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 of torsion groups which can occur on a smooth elliptic Calabi-Yau n-fold is contained in the set of subgroups which appear on a rational elliptic surface if n ≥ 3 and is slightly larger for n = 2. The key idea in our proof is showing that any elliptic fibration with sufficiently large torsion 1 has singularities in codimension 2 which

doi:10.1007/jhep04(2020)103
fatcat:ftimrypun5gbjj5h6gfwo4fkpe