Tall sections from non-minimal transformations

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.

16 pages

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Cited by in corpus (3)

• Non-Higgsable abelian gauge symmetry and F-theory on fiber products of rational elliptic surfaces
• Exotic matter on singular divisors in F-theory
• Discrete gauge groups in certain F-theory models in six dimensions