Tall sections from non-minimal transformations

Morrison, David R.; Park, Daniel S.

doi:10.1007/JHEP10(2016)033

Tall sections from non-minimal transformations

Journal Article · Mon Oct 10 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP10(2016)033· OSTI ID:1361523

Morrison, David R. ^[1]; Park, Daniel S. ^[2]

Univ. of California, Santa Barbara, CA (United States); Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
Rutgers Univ., Piscataway, NJ (United States)

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.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0010008

OSTI ID:: 1361523

Alternate ID(s):: OSTI ID: 22610491

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 10 Vol. 2016; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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