Rocky Mountain Journal of Mathematics

Arithmetic and geometry of rational elliptic surfaces

Cec[! \' i!]lia Salgado

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Abstract

Let $\mathscr {E}$ be a rational elliptic surface over a number field~$k$. We study the interplay between a geometric property, the configuration of its singular fibers, and arithmetic features such as its Mordell-Weil rank over the base field and its possible minimal models over~$k$.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 6 (2016), 2061-2076.

Dates
First available in Project Euclid: 4 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1483520438

Digital Object Identifier
doi:10.1216/RMJ-2016-46-6-2061

Mathematical Reviews number (MathSciNet)
MR3591272

Zentralblatt MATH identifier
1369.14046

Subjects
Primary: 14G99: None of the above, but in this section 14J26: Rational and ruled surfaces 14J27: Elliptic surfaces

Keywords
Elliptic surfaces minimal models over arbitrary fields elliptic fibrations

Citation

Salgado, Cec[! \' i!]lia. Arithmetic and geometry of rational elliptic surfaces. Rocky Mountain J. Math. 46 (2016), no. 6, 2061--2076. doi:10.1216/RMJ-2016-46-6-2061. https://projecteuclid.org/euclid.rmjm/1483520438


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