Built on

ETS Editrice, Pisa, 1989
R. Miranda, The basic theory of elliptic surfaces · 1989
Earlier work this paper cites.
T. Shioda, Mordell-Weil lattices and Galois representation. I
1989
Earlier work this paper cites.
T. Shioda, On the Mordell-Weil lattices
1990
Earlier work this paper cites.
C. Vafa, Evidence for F theory
1996
Earlier work this paper cites.
D. R. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds. 1
1996
Earlier work this paper cites.
D. R. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds. 2
1996
Earlier work this paper cites.
P. S. Aspinwall and D. R. Morrison, Point-like instantons on K3 orbifolds
1997
Earlier work this paper cites.

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2016

Tall sections from non-minimal transformations

Morrison, David R., Park, Daniel S.

Understand

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 $\mathbb{P}^{112}$.

Built on

ETS Editrice, Pisa, 1989
R. Miranda, The basic theory of elliptic surfaces · 1989
Earlier work this paper cites.
T. Shioda, Mordell-Weil lattices and Galois representation. I
1989
Earlier work this paper cites.
T. Shioda, On the Mordell-Weil lattices
1990
Earlier work this paper cites.
C. Vafa, Evidence for F theory
1996
Earlier work this paper cites.
D. R. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds. 1
1996
Earlier work this paper cites.
D. R. Morrison and C. Vafa, Compactifications of F theory on Calabi-Yau threefolds. 2
1996
Earlier work this paper cites.
P. S. Aspinwall and D. R. Morrison, Point-like instantons on K3 orbifolds
1997
Earlier work this paper cites.