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Title: 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:
 [1];  [2]
  1. Univ. of California, Santa Barbara, CA (United States)
  2. 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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