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arXiv · 1606.07444

Tall sections from non-minimal transformations

David R. Morrison·Daniel S. Park
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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 $\mathbb{P}^{112}$ 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 $\mathbb{P}^{112}$ 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 $\mathbb{P}^{112}$. In particular, we show that the elliptic fibrations studied recently by Klevers and Taylor fall into this class of models.

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David R. Morrison, Daniel S. Park. 2016-06-23. Tall sections from non-minimal transformations. https://doi.org/10.1007/jhep10(2016)033

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