# Tall sections from non-minimal transformations

## Abstract

In previous study, 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 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 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 P ^{112}. In particular, we show that the elliptic fibrations studied recently by Klevers and Taylor fall into this class of models.

- Authors:

- Univ. of California, Santa Barbara, CA (United States)
- Rutgers Univ., Piscataway, NJ (United States)

- Publication Date:

- Research Org.:
- Univ. of California, Santa Barbara, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1361523

- Grant/Contract Number:
- [SC0010008]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- [Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 10]; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; differential and algebraic geometry; F-theory; gauge symmetry; superstring vacua

### Citation Formats

```
Morrison, David R., and Park, Daniel S. Tall sections from non-minimal transformations. United States: N. p., 2016.
Web. doi:10.1007/JHEP10(2016)033.
```

```
Morrison, David R., & Park, Daniel S. Tall sections from non-minimal transformations. United States. doi:10.1007/JHEP10(2016)033.
```

```
Morrison, David R., and Park, Daniel S. Mon .
"Tall sections from non-minimal transformations". United States. doi:10.1007/JHEP10(2016)033. https://www.osti.gov/servlets/purl/1361523.
```

```
@article{osti_1361523,
```

title = {Tall sections from non-minimal transformations},

author = {Morrison, David R. and Park, Daniel S.},

abstractNote = {In previous study, 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 P112 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 P112 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 P112. In particular, we show that the elliptic fibrations studied recently by Klevers and Taylor fall into this class of models.},

doi = {10.1007/JHEP10(2016)033},

journal = {Journal of High Energy Physics (Online)},

number = [10],

volume = [2016],

place = {United States},

year = {2016},

month = {10}

}

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