Abstract
In previous work, we have shown that elliptic fibrations with two sections, or Mordell-Weil rank one, can always be mapped birationally to a Weierstrass model of a certain form, namely, the Jacobian of a \( {\mathrm{\mathbb{P}}}^{112} \) model. Most constructions of elliptically fibered Calabi-Yau manifolds with two sections have been carried out assuming that the image of this birational map was a “minimal” Weierstrass model. In this paper, we show that for some elliptically fibered Calabi-Yau manifolds with Mordell-Weil rank-one, the Jacobian of the \( {\mathrm{\mathbb{P}}}^{112} \) model is not minimal. Said another way, starting from a Calabi-Yau Weierstrass model, the total space must be blown up (thereby destroying the “Calabi-Yau” property) in order to embed the model into \( {\mathrm{\mathbb{P}}}^{112} \). In particular, we show that the elliptic fibrations studied recently by Klevers and Taylor fall into this class of models.
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Morrison, D.R., Park, D.S. Tall sections from non-minimal transformations. J. High Energ. Phys. 2016, 33 (2016). https://doi.org/10.1007/JHEP10(2016)033
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DOI: https://doi.org/10.1007/JHEP10(2016)033